def cij(i, j, a, b):
    assert len(a[0]) == len(b)
    N = len(b)
    #print("sum")
    #[print(f"  a[{i}][{n}] * b[{n}][{j}]") for n in range(N)]
    return sum(
        a[i][n] * b[n][j]
        for n in range(N)
    )

def mult(a, b):
    return [
        [
            cij(i, j, a, b)
            for j in range(len(b[0]))
        ]
        for i in range(len(a))
    ]

genmat1 = [[1, 0, 0, 0, 1, 1, 0],
           [0, 1, 0, 0, 1, 0, 1],
           [0, 0, 1, 0, 0, 1, 1],
           [0, 0, 0, 1, 1, 1, 1]]

genmat = [[1, 1, 1, 0, 0, 0, 0, 1],
          [1, 0, 0, 1, 1, 0, 0, 1],
          [0, 1, 0, 1, 0, 1, 0, 1],
          [1, 1, 0, 1, 0, 0, 1, 0]]

a = [[1, 0, 1, 1]]

def gendat():
    def do(i):
        for bit in reversed(range(4)):
            b = i >> bit & 1
            yield b
    for i in range(16):
        yield [list(do(i))]

for mat in gendat():
    m2 = mult(mat, genmat1)
    print(m2, end=' ')
    ext = sum(m2[0])
    print(ext, ext % 2, end=' | ')
    ext1 = sum(mat[0][0:3])
    print(ext1, ext1 % 2)

#   [1, 0, 1, 1, 2, 3, 2, 3]

chkmat = [[1, 0, 1, 0, 1, 0, 1, 0],
          [0, 1, 1, 0, 0, 1, 1, 0],
          [0, 0, 0, 1, 1, 1, 1, 0],
          [1, 1, 1, 1, 1, 1, 1, 1]]

b = [[0],
     [1],
     [1],
     [0],
     [0],
     [1],
     [1],
     [0]]

#print(mult(chkmat, b))