New best equivocation codes for syndrome coding

Abstract

In this paper we present a code design technique which produces codes for syndrome coding which have better secrecy than the best error correcting codes. Code examples are given for the case where the number of parity bits of the code is equal to 15. The code design technique presented is based on extensions of the parity check matrix of a set of good equivocation codes of shorter length. It is also shown that syndrome coding can be implemented without the traditional syndrome look up table, enabling any length codes to be used. An efficient recursive method to calculate the equivocation rate for the binary symmetric channel (BSC) and any linear binary code is also presented. The design results show that the best equivocation codes (BEC) that are produced have better equivocation rate for the syndrome coding scheme compared to all previously published codes, including the best known codes (BKC).