The binary self-dual codes of length up to 32: A revised enumeration

This paper presents a revised enumeration of the binary self-dual codes of length up to 32 given by Conway and Pless in 1978–1980. The list of 85 doubly-even self-dual codes of length 32 is essentially correct, but several of their descriptions need amending. The principal change is that there are 7...

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Bibliographic Details
Published inJournal of combinatorial theory. Series A Vol. 60; no. 2; pp. 183 - 195
Main Authors Conway, J.H, Pless, V, Sloane, N.J.A
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 01.07.1992
Academic Press
Subjects
Algebra
Exact sciences and technology
Mathematics
Number theory
Sciences and techniques of general use
Binary code
Enumeration
Automorphism group
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Summary:This paper presents a revised enumeration of the binary self-dual codes of length up to 32 given by Conway and Pless in 1978–1980. The list of 85 doubly-even self-dual codes of length 32 is essentially correct, but several of their descriptions need amending. The principal change is that there are 731 (not 664) inequivalent self-dual codes of length 30. Furthermore, there are three (not two) [28, 14, 6] and 13 (not eight) [30, 15, 6] self-dual codes. Some additional information is provided about the self-dual codes of length less than 32.
ISSN:0097-3165
1096-0899
DOI:10.1016/0097-3165(92)90003-D