[TSG 2021] Advanced Fisher

While "the god" rkm0959 taken down Crypto and PPC, I only solved this one :p

 

Compared to "baby version", the frequency is changed(439.97Hz -> 440Hz)

 

Since 2205 * 440 % 44100 == 0, wave[i] = wave[i+2205] for all i, which means that there are only 2205 of the unique values. Then priori approach seems not capable of this version. But by following below steps, this prob can be transformed as the system of the linear equations.

Step 1.

generate test.wav file such that no shuffle / wave[i] = np.sin(i * 440 / 44100 * (2 * np.pi))

wave = np.empty(473 * 2000)
for i in range(len(wave)):
  wave[i] = np.sin(i * 440 / 44100 * (2 * np.pi))
sf.write('test.wav', wave, 44100, 'PCM_24')

Step 2.

Parse test.wav, find 2205 unique values. It is required to adjust the small error during convert & save wav files.

frames, samplerate = sf.read('./test.wav')
mapping = {}
T = 2205
for i in range(T):
  mapping[frames[i]] = i

Step 3.

Count the occurance of the each frequency of result.wav.

cnt = [0]*T
S2 = set()
for frame in frames2:
  cnt[mapping[frame]] += 1
print(cnt)

'''
[444230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, ..., 229, 229, 229]
'''

Step 4.

If signals[i] == 0, then cnt[i*2000:(i+1)*2000] += 1. This is the most important observation. But we have 473 unknown variables(signals[i]) and 441 known equations(You may wonder why the number of equation is 441, not 2205. But equation for cnt[5k] = cnt[5k+1] = cnt[5k+2] = cnt[5k+3] = cnt[5k+4]. So the number of equation is 2205/5 = 441).

 

Fortunately, we know the flag starts with TSGCTF{. So the number of the unknown variables are decreased 473 to 400. Then the system of the linear equations becomes solvable.

 

(eliminate TSGCTF{ part)

v1 = string_to_signals('TSGCTF{') # len 73  
L1 = [230, 230, 230, ..., 229, 229]
L2 = [L1[i] for i in range(0,len(L1),5)]
print(len(L1), len(L2))

for i in range(73):
  if v1[i] == 0: continue
  idx = i*400 % 441
  for j in range(400):
    L2[(idx+j)%441] -= 1

print(L2)

(solve linear equation)

from sage.all import *

B = vector([192, 192, 193, ... 191, 191, 192])
assert(len(B)==441)
M = [[0]*441 for i in range(441)]
for i in range(441):
  for j in range(400):
    M[i][(i+j)%441]=1

M = Matrix(ZZ, M)
A = M.solve_right(B)
print(A)

print(M*A==B)

# (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, ... 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1)

 

Step 5.

By using recovered signals, recover a flag. Beware of a re-indexing.

  seq = (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, ... 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1)
  original = []
  for i in range(34, 431):
    idx = i*400%441
    original.append(seq[idx])
  print(signals_to_string(original))

Unfortunately, my code is not well-formulated and may causes angry. It is divided into two separate files. I tried to merge this into an one file and enable to find a flag for a single execution but I don't have enough time. I'm just a poor graduate student. Please kindly understand this :(

 

chk.py

import soundfile as sf
import numpy as np
from utils import signals_to_string, string_to_signals

def attempt2():
  wave = np.empty(473 * 2000)
  for i in range(len(wave)):
    wave[i] = np.sin(i * 440 / 44100 * (2 * np.pi))
  #sf.write('test.wav', wave, 44100, 'PCM_24')
  frames, samplerate = sf.read('./test.wav')
  mapping = {}
  T = 2205
  for i in range(T):
    mapping[frames[i]] = i

  print(frames[:T] == frames[T:2*T])

  frames2, samplerate2 = sf.read('./result.wav')
  cnt = [0]*T
  S2 = set()
  for frame in frames2:
    cnt[mapping[frame]] += 1
  print(cnt)

'''
[444230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 
230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 
231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 
231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 
228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 
226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 223, 223, 223, 223, 223, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 
225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 
226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 
229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 227, 227, 
227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 
229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 
226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 
227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 
230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 
231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 
227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 
228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 
229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 
229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 
227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 
225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 224, 224, 224, 224, 224, 223, 223, 223, 223, 223, 224, 224, 224, 224, 224, 224, 
224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 
224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 
228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 
228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229]
'''

# 222 of zero, 251 of one

def attempt3():
  frames, samplerate = sf.read('./test.wav')
  mapping = {}
  T = 2205
  for i in range(T):
    mapping[frames[i]] = i
  v1 = string_to_signals('TSGCTF{') # len 73  
  L1 = [230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 223, 223, 223, 223, 223, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 232, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 231, 230, 230, 230, 230, 230, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 230, 230, 230, 230, 230, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225,  225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 224, 224, 224, 224, 224, 223, 223, 223, 223, 223, 224, 224, 224, 224, 224, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 224, 224, 224, 224, 224, 225, 225, 225, 225, 225, 225, 225, 225, 225, 225, 226, 226, 226, 226, 226, 226, 226, 226, 226, 226, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 227, 227, 227, 227, 227, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 228, 229, 229, 229, 229, 229]
  L2 = [L1[i] for i in range(0,len(L1),5)]
  print(len(L1), len(L2))

  for i in range(73):
    if v1[i] == 0: continue
    idx = i*400 % 441
    for j in range(400):
      L2[(idx+j)%441] -= 1

  print(L2)

def attempt4():
  seq = (0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1)
  original = []
  for i in range(34, 431):
    idx = i*400%441
    original.append(seq[idx])
  print(signals_to_string(original))

#signals_to_string('1110001010101000100011101010101011100011100010111010001010111000100011101010101011100010101110100010111011101110111000101010001010101000100010111010001110111000101010101110001110100011101010101011100010101110001010101010001010101110111000101010001110101010101110001110111000111011101110111011100010111010001010100010001110101010101110001110101110100011101110111000111010100010001110101110111010111')
attempt4()

linear.py

from sage.all import *

B = vector([192, 192, 193, 193, 193, 193, 194, 193, 194, 193, 194, 193, 193, 193, 193, 194, 193, 194, 193, 193, 193, 193, 193, 192, 193, 193, 194, 193, 194, 193, 193, 192, 192, 193, 193, 193, 193, 194, 193, 194, 193, 194, 194, 193, 193, 192, 192, 192, 193, 192, 193, 192, 192, 192, 191, 191, 190, 190, 189, 190, 190, 191, 191, 191, 192, 191, 191, 191, 192, 192, 192, 192, 193, 193, 193, 193, 193, 193, 192, 192, 191, 191, 191, 191, 192, 191, 192, 191, 191, 190, 190, 189, 189, 189, 189, 189, 188, 189, 189, 190, 189, 190, 189, 190, 190, 189, 190, 189, 189, 188, 188, 188, 189, 189, 189, 189, 188, 189, 188, 189, 189, 189, 189, 189, 189, 188, 189, 188, 189, 188, 189, 189, 190, 190, 191, 191, 191, 191, 191, 192, 191, 192, 191, 192, 191, 191, 192, 191, 191, 190, 191, 190, 191, 190, 190, 190, 189, 189, 188, 189, 188, 189, 189, 190, 189, 189, 190, 189, 189, 189, 190, 190, 191, 190, 191, 190, 190, 191, 191, 191, 190, 191, 190, 191, 190, 191, 191, 190, 190, 190, 190, 190, 191, 190, 191, 190, 190, 191, 191, 191, 190, 191, 190, 191, 191, 191, 191, 191, 191, 191, 191, 190, 190, 190, 191, 191, 192, 192, 192, 193, 192, 193, 193, 194, 194, 194, 193, 193, 194, 194, 195, 195, 195, 194, 194, 193, 194, 194, 194, 195, 195, 195, 194, 194, 194, 194, 194, 194, 194, 194, 195, 194, 194, 193, 193, 193, 193, 192, 192, 192, 191, 192, 191, 191, 190, 190, 190, 190, 190, 189, 190, 189, 190, 189, 190, 190, 191, 190, 190, 190, 189, 190, 190, 191, 191, 191, 190, 191, 191, 190, 191, 190, 191, 191, 192, 191, 191, 190, 190, 190, 189, 190, 189, 190, 189, 190, 189, 190, 190, 190, 191, 191, 191, 190, 190, 189, 190, 189, 190, 190, 189, 190, 189, 190, 189, 190, 189, 190, 189, 189, 189, 188, 189, 188, 189, 188, 188, 187, 188, 188, 188, 188, 187, 188, 187, 187, 186, 186, 186, 187, 187, 186, 186, 186, 186, 186, 187, 186, 187, 186, 186, 187, 186, 187, 186, 186, 185, 185, 185, 185, 185, 185, 186, 185, 186, 186, 187, 187, 188, 187, 188, 188, 188, 189, 188, 189, 189, 189, 189, 189, 189, 189, 189, 188, 189, 189, 190, 190, 190, 189, 189, 189, 188, 189, 189, 190, 190, 191, 191, 191, 191, 191, 192, 192, 193, 192, 192, 191, 192, 191, 191, 190, 190, 191, 190, 191, 190, 191, 191, 192, 191, 191, 191, 191, 192, 191, 192, 191, 191, 191, 192])
assert(len(B)==441)
M = [[0]*441 for i in range(441)]
for i in range(441):
  for j in range(400):
    M[i][(i+j)%441]=1

M = Matrix(ZZ, M)
A = M.solve_right(B)
print(A)

print(M*A==B)

#(0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1)