Classification of Formally Self-Dual even Codes of Lengths up to 16

Koichi Betsumiya; Masaaki Harada

doi:10.1023/A:1011223128089

Classification of Formally Self-Dual even Codes of Lengths up to 16

Koichi Betsumiya, Masaaki Harada

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

In this note, we give the complete classification of binary formally self-dual even codes of lengths 10, 12, 14 and 16. There are exactly fourteen, 29, 99 and 914 inequivalent such codes of lengths 10, 12, 14 and 16, respectively. This completes the classification of formally self-dual even codes of lengths up to 16. The first example of a formally self-dual even code with a trivial automorphism group is also found. This shows that 16 is the smallest length for which there is a formally self-dual even code with a trivial automorphism group.

Original language	English
Pages (from-to)	325-332
Number of pages	8
Journal	Designs, Codes, and Cryptography
Volume	23
Issue number	3
DOIs	https://doi.org/10.1023/A:1011223128089
Publication status	Published - 2001 Aug 1
Externally published	Yes

Keywords

Automorphism groups
Classification
Formally self-dual even codes

ASJC Scopus subject areas

Computer Science Applications
Applied Mathematics

Access to Document

10.1023/A:1011223128089

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abstract = "In this note, we give the complete classification of binary formally self-dual even codes of lengths 10, 12, 14 and 16. There are exactly fourteen, 29, 99 and 914 inequivalent such codes of lengths 10, 12, 14 and 16, respectively. This completes the classification of formally self-dual even codes of lengths up to 16. The first example of a formally self-dual even code with a trivial automorphism group is also found. This shows that 16 is the smallest length for which there is a formally self-dual even code with a trivial automorphism group.",

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N2 - In this note, we give the complete classification of binary formally self-dual even codes of lengths 10, 12, 14 and 16. There are exactly fourteen, 29, 99 and 914 inequivalent such codes of lengths 10, 12, 14 and 16, respectively. This completes the classification of formally self-dual even codes of lengths up to 16. The first example of a formally self-dual even code with a trivial automorphism group is also found. This shows that 16 is the smallest length for which there is a formally self-dual even code with a trivial automorphism group.

AB - In this note, we give the complete classification of binary formally self-dual even codes of lengths 10, 12, 14 and 16. There are exactly fourteen, 29, 99 and 914 inequivalent such codes of lengths 10, 12, 14 and 16, respectively. This completes the classification of formally self-dual even codes of lengths up to 16. The first example of a formally self-dual even code with a trivial automorphism group is also found. This shows that 16 is the smallest length for which there is a formally self-dual even code with a trivial automorphism group.

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