Designs, Codes and Cryptography

, Volume 86, Issue 5, pp 1085–1094 | Cite as

Binary extremal self-dual codes of length 60 and related codes

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Abstract

We give a classification of four-circulant singly even self-dual [60, 30, d] codes for \(d=10\) and 12. These codes are used to construct extremal singly even self-dual [60, 30, 12] codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. From extremal singly even self-dual [60, 30, 12] codes, we also construct optimal singly even self-dual [58, 29, 10] codes with weight enumerator for which no optimal singly even self-dual code was previously known to exist. Finally, we give some restriction on the possible weight enumerators of certain singly even self-dual codes with shadow of minimum weight 1.

Keywords

Extremal self-dual code Weight enumerator Neighbor 

Mathematics Subject Classification

94B05 

Notes

Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 15H03633. The author would like to thank the anonymous reviewers for the useful comments.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Research Center for Pure and Applied Mathematics, Graduate School of Information SciencesTohoku UniversitySendaiJapan

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