Dissections and Constant Weight Codes

Abstract

The problem of encoding and decoding binary block codes of length n and constant Hamming weight w is formulated as a polytope dissection problem. This is done by working with a w-dimensional Euclidean space representation for the information and code vectors. Novel algorithms based on two new dissections are presented. The first is a dissection of a subset of the codebook, and has time-complexity o(w). The second is a dissection of the entire codebook, and has time-complexity o(w log w). Implementation issues associated with the second algorithm are discussed in detail