Shape Enumerators of Self-Dual NRT Codes over Finite Fields
Abstract.
We use invariant theory of finite groups to study shape enumerators of self-dual linear codes in a finite NRT metric space. We provide a new approach that avoids applying Molien’s formula to compute all possible shape enumerators. We also explicitly compute the shape enumerators of some low-dimensional self-dual NRT codes over an arbitrary finite field.
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Acknowledgments.
The authors would like to thank the anonymous referees and the editor for their careful reading, constructive comments, and suggestions. The first author would like thank Professor Simon Xu for his helpful conversations and encouragement.
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Information & Authors
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Published In
SIAM Journal on Discrete Mathematics
Pages: 2841 - 2854
DOI: 10.1137/24M1633376
ISSN (online): 1095-7146
Copyright
© 2024 Society for Industrial and Applied Mathematics.
History
Submitted: 22 January 2024
Accepted: 5 August 2024
Published online: 8 November 2024
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Funding Information
Algoma University: AURF-PT-40370-71
Funding: This research was partially supported by Algoma University under grant AURF-PT-40370-71.
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