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Relative Generalized Hamming Weights and Extended Weight Polynomials of Almost Affine Codes

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Coding Theory and Applications (ICMCTA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10495))

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Abstract

This paper is devoted to giving a generalization from linear codes to the larger class of almost affine codes of two different results. One such result is how one can express the relative generalized Hamming weights of a pair of codes in terms of intersection properties between the smallest of these codes and subcodes of the largest code. The other result tells how one can find the extended weight polynomials, expressing the number of codewords of each possible weight, for each code in an infinite hierarchy of extensions of a code over a given alphabet. Our tools will be demi-matroids and matroids.

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Authors and Affiliations

  1. UiT - The Arctic University of Norway, 9037, Tromsø, Norway

    Trygve Johnsen & Hugues Verdure

Authors
  1. Trygve Johnsen
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  2. Hugues Verdure
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Correspondence to Trygve Johnsen .

Editor information

Editors and Affiliations

  1. University of Valladolid, Valladolid, Spain

    Ángela I. Barbero

  2. University of Tartu, Tartu, Estonia

    Vitaly Skachek

  3. Simula@UiB and University of Bergen, Bergen, Norway

    Øyvind Ytrehus

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Johnsen, T., Verdure, H. (2017). Relative Generalized Hamming Weights and Extended Weight Polynomials of Almost Affine Codes. In: Barbero, Á., Skachek, V., Ytrehus, Ø. (eds) Coding Theory and Applications. ICMCTA 2017. Lecture Notes in Computer Science(), vol 10495. Springer, Cham. https://doi.org/10.1007/978-3-319-66278-7_17

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  • DOI: https://doi.org/10.1007/978-3-319-66278-7_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66277-0

  • Online ISBN: 978-3-319-66278-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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