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MacWilliams extension property for arbitrary weights on linear codes over module alphabets

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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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Authors and Affiliations

  1. Independent Researcher, Rijswijk, South Holland, The Netherlands

    Serhii Dyshko

  2. Western Michigan University, Kalamazoo, MI, USA

    Jay A. Wood

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  1. Serhii Dyshko
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  2. Jay A. Wood
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Correspondence to Jay A. Wood.

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In memoriam: Vera Pless, 1931–2020.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless”

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Dyshko, S., Wood, J.A. MacWilliams extension property for arbitrary weights on linear codes over module alphabets. Des. Codes Cryptogr. 90, 2683–2701 (2022). https://doi.org/10.1007/s10623-021-00945-w

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