A systematic construction of self-dual codes

Authors:
J. -C. Carlach;A. Otmani
Affiliations:
DMR/DDH, France-Telecom R&D, Cesson-Sevigne, France;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

A new coding construction scheme of block codes using short base codes and permutations that enables the construction of binary self-dual codes is presented in Cadic et al. (2001) and Carlach et al. (1999, 2000). The scheme leads to doubly-even (resp,. singly-even) self-dual codes provided the base code is a doubly-even self-dual code and the number of permutations is even (resp., odd). We study the particular case where the base code is the [8, 4, 4] extended Hamming. In this special case, we construct a new [88, 44, 16] extremal doubly-even self-dual code and we give a new unified construction of the five [32, 16, 8] extremal doubly-even self-dual codes.