February Fourier Talks 2007

Vinay Vaishampayan


Dissections and Constant Weight Codes


(Joint work: Chao Tian, N. J. A. Sloane)

While dissection problems have been a subject of interest to geometers for a long time, it is only recently that applications to coding have become known. In this talk, we consider the problem of encoding and decoding binary block codes of length n and constant Hamming weight $w$. We show that this problem can be formulated as a polytope dissection problem by working with an appropriate w-dimensional Euclidean space representation for the codebook. Several dissections will be described, along with resulting algorithms and technical problems that are encountered along the way. In particular, an interesting connection to integer-integer transforms, used in signal processing, will be described.