Lexicodes

Lexicodes were introducted by Conway and Sloane in [CS]. They form a class of binary codes which are (a) non necessarily linear, (b) in general hard to construct, (c) in general hard to encode and decode. Why study them then? There are several reasons: (a) they often times are linear, (b) they have excellent parameters, (c) one might hope that with further investigation, someone (maybe the person reading this) may in the future discover fast ending and decoding algorithms. One other reason: they have fascinating connections to combinatorial game theory (such as the game of nim, which we have seen already).