Decoding generalised hyperoctahedral groups and asymptotic analysis of correctible error patterns

We demonstrate a majority-logic decoding algorithm for decoding the generalised hyperoctahedral group $C_m \wr S_n$ when thought of as an error-correcting code. We also find the complexity of this decoding algorithm and compare it with that of another, more general, algorithm. Finally, we enumerate the number of error patterns exceeding the correction capability that can be successfully decoded by this algorithm, and analyse this asymptotically.

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