Near-Extremal Formally Self-Dual Even Codes of Lengths 24 and 32

Authors:
T. Aaron Gulliver;Masaaki Harada;Takuji Nishimura;Patric R. Östergård
Affiliations:
Department of Electrical and Computer Engineering, University of Victoria, Victoria, Canada V8W 3P6;Department of Mathematical Sciences, Yamagata University, Yamagata, Japan 990---8560;Department of Mathematical Sciences, Yamagata University, Yamagata, Japan 990---8560;Department of Electrical and Communications Engineering, Helsinki University of Technology, HUT, Finland 02015
Venue:
Designs, Codes and Cryptography
Year:
2005

Citing 2
Cited 2

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Nonexistence of near-extremal formally self-dual even codes of length divisible by 8

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A note on formally self-dual even codes of length divisible by 8

Finite Fields and Their Applications

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Abstract

The weight enumerator of a formally self-dual even code is obtained by the Gleason theorem. Recently, Kim and Pless gave some restrictions on the possible weight enumerators of near-extremal formally self-dual even codes of length divisible by eight. In this paper, the weight enumerators for which there is a near-extremal formally self-dual even code are completely determined for lengths 24 and 32, by constructing new near-extremal formally self-dual codes. We also give a classification of near- extremal double circulant codes of lengths 24 and 32.