Quaternary affine variety codes over a Klein-like curve

Nupur Patanker () and Sanjay Kumar Singh ()
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Nupur Patanker: Indian Institute of Science Education and Research
Sanjay Kumar Singh: Indian Institute of Science Education and Research

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 1-14

Abstract: Abstract In this note, we study primary monomial affine variety codes defined from the Klein-like curve $$x^{2}y+y^{2}+x$$ x 2 y + y 2 + x over $$\mathbb {F}_{4}$$ 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].

Keywords: Affine variety codes; Groebner basis; Klein-like curves; Generalized Hamming weights; Symbol-pair distance; 94B27; (13P10; 11T71) (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00522-y

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