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Enumeration formulae for self-dual, self-orthogonal and complementary-dual quasi-cyclic codes over finite fields

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Abstract

Let \(\mathbb {F}_{q}\) denote the finite field of order q, and let ℓ,m be positive integers with \(\gcd (m,q)=1.\) In this paper, we enumerate all self-orthogonal, self-dual and complementary-dual ℓ-quasi-cyclic codes of length m ℓ over \(\mathbb {F}_{q}\) by placing the Euclidean inner product on \(\mathbb {F}_{q}^{m\ell }.\)

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Authors and Affiliations

  1. Department of Mathematics, IIIT-Delhi, Delhi, India

    Anuradha Sharma

  2. Department of Mathematics, IIT Delhi, Delhi, India

    Taranjot Kaur

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  1. Anuradha Sharma
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  2. Taranjot Kaur
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Correspondence to Anuradha Sharma.

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Sharma, A., Kaur, T. Enumeration formulae for self-dual, self-orthogonal and complementary-dual quasi-cyclic codes over finite fields. Cryptogr. Commun. 10, 401–435 (2018). https://doi.org/10.1007/s12095-017-0228-7

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  • DOI: https://doi.org/10.1007/s12095-017-0228-7

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Mathematics Subject Classification (2010)