Abstract

. Generalized Hamming weight hierarchies and permutation-optimal trellis decoders are found for several extremal self-dual codes. The latter problem involves finding chains of subcodes that allow construction of a uniformly efficient permutation. The task of finding such chains of subcodes is shown to be substantially simplifiable in the case of self-dual codes in general, and is particularly straightforward when certain subcodes meet the Griesmer bound with equality. These results are used to characterize the permutation-optimal trellises and generalized Hamming weights for all [32; 16;8] binary self-dual codes and for several other codes. The number of uniformly efficient permutations for the [24; 12;8]Golay code, and a lower bound on the number for the [48; 24;12] quadratic residue code, are found. Keywords: Chain condition, Conway-Pless codes, double chain condition, generalized Hamming weights, unique codes. 1. Introduction Representations of block codes by trellises allow comput...

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