#! /usr/local/bin/sage
### -*-python-*-

k = GF(2)

def memoize(f):
  memo = dict()
  def _(*args):
    try:
      return memo[args]
    except KeyError:
      r = f(*args)
      memo[args] = r
      return r
  return _

@memoize
def Abase(w, c):
  return matrix(k, [[j == i for j in xrange(w)]
                    for i in xrange(w)] +
                   [[j == i or j == i + c for j in xrange(w)]
                    for i in xrange(w)])

@memoize
def A(w, c, i): return Abase(w, c)[i:i + w, 0:w]

def B(w, c, i, j): return A(w, c, i) + A(w, c, j)

def urank(w, c, i): return A(w, c, i).rank()

def domlen(w, c):
  for i in xrange(w):
    if urank(w, c, i) < w: return ZZ(i)
    for j in xrange(i):
      if B(w, c, i, j).rank() < w: return ZZ(i)
  return ZZ(w) #unlikely

def shifts(w):
  for c1 in xrange(0, 8):
    for c8 in xrange(w - 8, -8, -8):
      yield c8 + c1

def stretch_shift(w):
  want_bits = (w - 1).nbits()
  best_bits, best_dom, best_c = 0, 0, -1
  for c in shifts(w):
    d = domlen(w, c)
    bits = d.nbits()
    if bits == want_bits: return c, d
    elif bits > best_bits: best_bits, best_dom, best_c = bits, d, c
  return best_c, best_dom

for w in [64, 96, 128, 192, 256, 512]:
  c, dom = stretch_shift(w)
  print '%3d: %3d [%d]' % (w, c, dom)