Coding scheme for a wire-tap channel using regular codes (Q1068785)

Coset-coding was suggested by J. M. Goethals and L. Huguet as a coding scheme for the purpose of confusing a wire-tapper. This scheme is based on the decomposition \(C/C_ 0=\{C(0),...,C(i),...,C(M-1)\}\) of a binary code C with respect to a proper subcode \(C_ 0\), where each vector in the same coset C(i) conveys the same information. \textit{P. Delsarte's} decoding function [IEEE Trans. Inf. Theory IT-24, 70- 75 (1978; Zbl 0369.94010)], which decodes the received vector as the vector maximizing a so-called decision function \(\Delta\), obtained by partial syndromes, is easily computed from the weight enumerator of \(C_ 0^{\perp}\), when it is a regular code. Some examples are presented concerning the Hamming and 2-error correcting BCH codes, which are completely regular.