Elsevier

Discrete Mathematics

Volume 56, Issues 2–3, October 1985, Pages 191-201
Discrete Mathematics

Coding scheme for a wire-tap channel using regular codes

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Abstract

Coset-coding was suggested by Goethals and Huguet [3] as a coding scheme for the purpose of confusing a wire-tapper. This scheme is based on the decomposition C/C0= {C(0),...,C(i),...,C(M-1)} of a binary code C with respect to a proper subcode C0, where each vector in the same coset C(i) conveys the same information.

Delsarts' decoding function [1], which decodes the received vector as the vector maximizing a so-called decision function Δ, obtained by partial syndromes, is easily computed from the weight enumerator of C0, when it is a regular code. Some examples are presented concerning the Hamming and 2-error correcting BCH codes, which are completely regular.

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