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Quaternary affine variety codes over a Klein-like curve

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Abstract

In this note, we study primary monomial affine variety codes defined from the Klein-like curve \(x^{2}y+y^{2}+x\) over \(\mathbb {F}_{4}\). Implementing the techniques suggested by Geil and Özbudak in [3], we estimate the minimum distance of various considered codes. In a few cases, we obtain the exact value of the symbol-pair distance of these codes. Furthermore, we determine lower bounds on the generalized Hamming weights of the codes so obtained. Few codes obtained are the best-known codes according to [5].

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Acknowledgements

We would like to thank Dr. Mrinmoy Datta for reading the manuscript and providing his valauble suggestions.

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

    Nupur Patanker & Sanjay Kumar Singh

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  1. Nupur Patanker
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  2. Sanjay Kumar Singh
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Correspondence to Nupur Patanker.

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Patanker, N., Singh, S.K. Quaternary affine variety codes over a Klein-like curve. Indian J Pure Appl Math 55, 1–14 (2024). https://doi.org/10.1007/s13226-023-00522-y

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