Abstract
In this paper, an expression for the undetected error probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(P\epsilon)</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(P\epsilon)</tex> and the corresponding maximizing ε are given.
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