Constant weight codes: a geometric approach

We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight of the code. The encoder and decoder mappings are then interpreted as a bijection between a certain hyper-rectangle and a polytope in this Euclidean space. An inductive dissection algorithm is developed for constructing such a bijection. We prove that the algorithm is correct and analyze its complexity. The complexity of the proposed algorithm depends on the weight of the code, rather than on the block length as in previous algorithms. This approach is advantageous when the weight is smaller than the square root of the block length