Checks that the encoding described in the page bellow is resilient to rotations. https://github.com/polyvision/EasyRaceLapTimer/blob/master/docs/ir_pulses.md

check_encoding.py

def encode(n):
	if (n > 63) | (n < 0):
		raise Exception('Out of range {0}'.format(n))
	ret = [digit for digit in bin(n)[2:]] # [2:] to chop off the "0b" part 
	ret += [reduce(lambda a,b: '1' if (a != b) else '0', ret)]
	return ''.join(['0'] * (9 - len(ret)) + ret)

def rotate(l,n):
    return l[n:] + l[:n]

legal = frozenset(map(encode, range(0,63)))
for x in legal:
	for rot in range(1,8):
		if rotate(x, rot) in legal:
			print 'Found that {0} in rotation {1} is equal to {2}'.format(x, rot, rotate(x, rot))