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The Existence of a Self-Dual [70, 35, 12] Code and Formally Self-Dual Codes

✍ Scribed by Masaaki Harada

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 224 KB
Volume: 3
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1996.0174

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✦ Synopsis

In this note, the existence of self-dual codes and formally self-dual even codes is investigated. A construction for self-dual codes is presented, based on extending generator matrices. Using this method, a singly-even self-dual [70, 35, code is constructed from a self-dual code of length 68. This is the first published example of a singly-even [70, 35, code. Constructions are also given for formally selfdual even codes. Extremal formally self-dual even codes are constructed.

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All (Hermitian) self-dual [24,12,8] quaternary codes which have a non--trivial automorphism of order 3 are obtained up to equivalence. There exist exactly 205 inequivalent such codes. The codes under consideration are optimal, self-dual, and have the highest possible minimum distance for this length