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Special LCD codes from products of graphs

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We examine the binary codes from the adjacency matrices of various products of graphs, and show that if the binary codes of a set of graphs have the property that their dual codes are the codes of the associated reflexive graphs, and are thus LCD, i.e. have zero hull, then, with some restrictions, the binary code of the product will have the same property. The codes are candidates for decoding using this property, or also, in the case of the direct product, by permutation decoding.

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Notes

  1. Note typographical error on p.338, l.-11, in [24]

  2. Note typographical error on p.341, l.-7, in [24]

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of the Western Cape, Bellville, 7535, South Africa

    W. Fish, J. D. Key & E. Mwambene

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  1. W. Fish
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  2. J. D. Key
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  3. E. Mwambene
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Fish, W., Key, J.D. & Mwambene, E. Special LCD codes from products of graphs. AAECC 34, 553–579 (2023). https://doi.org/10.1007/s00200-021-00517-4

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