How to generate binary lexicodes - 09/30/2005

Dejan

"Lexicodes are mysterious things."

Although their definition is very simple, a considerable amount of patterns can be observed in their structure. Some of the famous optimal codes, like Hamming codes and binary Golay code, are lexicodes. In this talk, I will present Lexicographic Construction an efficient method for generating Lexicodes, and explain the role of coset leaders in this process. I will continue with investigating the relation between coset leaders of several successive iterations of Lexicographic Construction and present some improvements of the algorithm. At the end, I will take advantage of some of the properties of the lexicodes to generate dimension-4 lexicodes by hand.