Evaluation of the Undetected Error Probability of Single Parity-Check Product Codes

In this paper, an expression for the undetected error probability
(P\epsilon)
of single parity-check product (SPCP) codes used for error detection over a binary symmetric channel is derived. It is shown that square SPCP codes need not obey a certain commonly used bound. Approximate expressions for the maximum
(P\epsilon)
and the corresponding maximizing ε are given.