Extension of the parity check matrix to construct the best equivocation codes for syndrome coding

In this paper, we present a code design technique that produces the best equivocation codes(BEqC) for the syndrome coding scheme. This technique is based on the extension of the parity check matrix of a good (BEqC), [n, k] code by selecting the two best columns that extend the length of the code. The goal of this construction is to improve the communication security by increasing the equivocation rate. An efficient recursive method which derives the syndrome probability distribution for a particular code is presented to determine the equivocation rate for the Binary Symmetric Channel(BSC). Analysis show that the (BEqC) that is produced by adding two columns gives better equivocation rate compared to those codes that are produced by the addition of one column in two phases.