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On Euclidean self-dual codes and isometry codes

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Abstract

In this paper, we provide new methods and algorithms to construct Euclidean self-dual codes over large finite fields. With the existence of a dual basis, we study dual preserving linear maps, and as an application, we use them to construct self-orthogonal codes over small finite prime fields using the method of concatenation. Many new optimal self-orthogonal and self-dual codes are obtained.

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Acknowledgements

The author would like to thank anonymous referees for their constructive comments that improve the quality of the paper.

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  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Lin Sok

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  1. Lin Sok
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Correspondence to Lin Sok.

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The author would like to declare that no conflict of interest exits in the submission of this manuscript, and manuscript is an original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part.

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This research work is supported by Anhui Provincial Natural Science Foundation with Grant No. 1908085MA04.

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Sok, L. On Euclidean self-dual codes and isometry codes. AAECC 33, 73–89 (2022). https://doi.org/10.1007/s00200-020-00434-y

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  • DOI: https://doi.org/10.1007/s00200-020-00434-y

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