Checks that the encoding described in in the following link 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 = bin(n)[2:] # [2:] to chop off the "0b" part # creating initial bit encoding (for bits 3-8)
	ret += reduce(lambda a,b: '1' if (a != b) else '0', ret) # adding checksum as bit 9
	pad = ''.join(['0'] * (9 - len(ret)))
	return pad + ret # padding with leading zeros by spec (for bits 1-2 and maybe more for lower ids)

def decode(arr):
	if (len(arr) != 9):
		raise Exception('Should be of size 9, got: {0}'.format(arr))
	if (arr[0] != '0') or (arr[1] != '0'):
		raise Exception('Illegal header, got: {0}'.format(arr))
	if (reduce(lambda a,b: '1' if (a != b) else '0', arr[2:-1]) != arr[-1]):
		raise Exception('Illegal checksum, got: {0}'.format(arr))
	ret = 0
	for bit in arr[2:-1]:
		ret = (ret << 1) | (bit == '1')
	return ret

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

legal = frozenset(map(encode, range(0,63)))
colliding = set()
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))
			colliding.add(x)
print('Ids which don’t collide: {0}'.format(map(decode, legal.difference(colliding))))
print('Encodings which collide: {0}'.format(colliding))