MacWilliams extension property for arbitrary weights on linear codes over module alphabets
Pages 2683 - 2701
Abstract
The first author recently proved the extension theorem for linear codes over integer residue rings equipped with the Lee or the Euclidean weight by introducing a determinant criterion that is dual to earlier approaches. In this paper we generalize his techniques to the context of linear codes over an alphabet that is a finite pseudo-injective module with a cyclic socle and is equipped with an arbitrary weight. The main theorem is a criterion for the weight to have the extension property.
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Index Terms
- MacWilliams extension property for arbitrary weights on linear codes over module alphabets
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© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021.
Publisher
Kluwer Academic Publishers
United States
Publication History
Published: 01 November 2022
Accepted: 31 August 2021
Revision received: 28 August 2021
Received: 19 February 2021
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