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Construction methods for Galois LCD codes over finite fields

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Abstract

In this article, first we present a method for constructing many Hermitian LCD codes from a given Hermitian LCD code, and then provide several methods which utilize either a given [n, k, d] linear code or a given [n, k, d] Galois LCD code to construct new Galois LCD codes with different parameters. Using these construction methods, we construct several new [n, k, d] ternary LCD codes with better parameters for \( 26\le n\le 40,\) and \(21 \le k\le 30 \). Also, optimal \( \textit{2} \)-Galois LCD codes over \( {\mathbb {F}}_{2^3} \) for code length, \( 1\le n\le 15 \) have been obtained. Finally, we extend some previously known results to the \(\sigma \)-inner product from Euclidean inner product.

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Acknowledgements

Prof. R. K. Sharma is ConsenSys Blockchain chair Professor. He thanks ConsenSys AG for the privilege. The first author is financially supported by Council of Scientific and Industrial Research (CSIR), New Delhi, Govt. of India under File No. 09/086(1407)/2019-EMR-I, and the Second author is supported by University Grant Commission (UGC), New Delhi, Govt. of India under the grant DEC18-417932.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Gyanendra K. Verma, Astha Agrawal & R. K. Sharma

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  1. Gyanendra K. Verma
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  2. Astha Agrawal
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  3. R. K. Sharma
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Correspondence to Gyanendra K. Verma.

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Verma, G.K., Agrawal, A. & Sharma, R.K. Construction methods for Galois LCD codes over finite fields. J. Appl. Math. Comput. 69, 4023–4043 (2023). https://doi.org/10.1007/s12190-023-01914-3

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  • DOI: https://doi.org/10.1007/s12190-023-01914-3

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