Puncturing, expurgating and expanding the q-ary BCH based robust codes

A code that can detect any non-zero error with probability greater than zero is called robust. The set of codewords that mask an error e determine its undetected error probability, Q(e). The maximal error masking probability is denoted by Q_mc. A robust code is called optimum if there is no other code with larger number of codewords with the same length and the same Q_mc. In this paper we present constructions of optimum and nearly optimum robust codes. The constructions are based on modifications of the BCH based check matrix codes. In particular, puncturing, expurgating and expanding the codes while preserving their robustness.