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Affine Variety Codes over a Hyperelliptic Curve

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Abstract

We estimate the minimum distance of primary monomial affine variety codes defined from a hyperelliptic curve \({x^5} + x - {y^2}\) over \(\mathbb{F}_7\). To estimate the minimum distance of the codes, we apply symbolic computations implementing the techniques suggested by Geil and Özbudak. For some of these codes, we also obtain the symbol-pair distance. Furthermore, lower bounds on the generalized Hamming weights of the constructed codes are obtained. The proposed method to calculate the generalized Hamming weights can be applied to any primary monomial affine variety codes.

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Acknowledgements

The authors are very grateful to the reviewer for his/her comments and suggestions, which help to improve the quality of the paper.

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Authors and Affiliations

  1. Indian Institute of Science Education and Research, Bhopal, India

    S. K. Singh

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  1. N. Patanker
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Translated from Problemy Peredachi Informatsii, 2021, Vol. 57, No. 1, pp. 96–111 https://doi.org/10.31857/S0555292321010058.

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Patanker, N., Singh, S.K. Affine Variety Codes over a Hyperelliptic Curve. Probl Inf Transm 57, 84–97 (2021). https://doi.org/10.1134/S0032946021010051

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  • DOI: https://doi.org/10.1134/S0032946021010051

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