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Classification of Self-dual Codes of Length 20 over \(\mathbb {Z}_4\) and Length at Most 18 over \(\mathbb {F}_2+u\mathbb {F}_2\)

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Cryptography and Coding (IMACC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11929))

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Abstract

In this paper, we give a precise description of Rains’ algorithm for classifying self-dual \(\mathbb {Z}_4\)-codes with a given residue code. We will use this to classify self-dual \(\mathbb {Z}_4\)-codes of length 20. A similar method is used to classify self-dual codes over \(\mathbb {F}_2+u\mathbb {F}_2\). We will update the table given by Han, Lee and Lee, of the data regarding the classification of self-dual codes over \(\mathbb {F}_2+u\mathbb {F}_2\).

R. A. L. Betty—Partially supported by Philippine National Oil Company.

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Authors and Affiliations

  1. Institute of Mathematics, University of the Philippines-Diliman, Quezon City, 1101, Philippines

    Rowena Alma L. Betty

  2. Graduate School of Information Sciences, Tohoku University, Sendai, 980–8579, Japan

    Akihiro Munemasa

Authors
  1. Rowena Alma L. Betty
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  2. Akihiro Munemasa
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Correspondence to Rowena Alma L. Betty .

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Editors and Affiliations

  1. Royal Holloway, University of London, London, UK

    Martin Albrecht

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Betty, R.A.L., Munemasa, A. (2019). Classification of Self-dual Codes of Length 20 over \(\mathbb {Z}_4\) and Length at Most 18 over \(\mathbb {F}_2+u\mathbb {F}_2\). In: Albrecht, M. (eds) Cryptography and Coding. IMACC 2019. Lecture Notes in Computer Science(), vol 11929. Springer, Cham. https://doi.org/10.1007/978-3-030-35199-1_4

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  • DOI: https://doi.org/10.1007/978-3-030-35199-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-35198-4

  • Online ISBN: 978-3-030-35199-1

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