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On the subfield subcodes of Hermitian codes

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Abstract

We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤  32 and length up to 215. We show that some of the subfield subcodes of Hermitian codes are at least as good as the previously known codes, and we show the existence of good long codes.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Denmark, 2800, Lyngby, Denmark

    Fernando Piñero

  2. Department of Mathematics, University of Puerto Rico-Rio Piedras, P.O. Box 70377, San Juan, PR, 00936-8377, USA

    Heeralal Janwa

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  1. Fernando Piñero
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  2. Heeralal Janwa
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Correspondence to Fernando Piñero.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding Theory and Applications”.

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Piñero, F., Janwa, H. On the subfield subcodes of Hermitian codes. Des. Codes Cryptogr. 70, 157–173 (2014). https://doi.org/10.1007/s10623-012-9736-9

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  • DOI: https://doi.org/10.1007/s10623-012-9736-9

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