Constructing optimal ternary constant-weight codes by placing pieces on chessboards

Abstract

We study the problem of constructing optimal ternary constant-weight codes with Hamming weight w and minimum distance d=2w-1. We reformulate the problem as a problem of placing pieces on an M/spl times/M chessboard so that three simple conditions are satisfied. Using this, we construct codes with minimal length for a given number of codewords.