New Quantum and LCD Codes over Finite Fields of Even Characteristic

Habibul Islam; Om Prakash

doi:10.14429/dsj.71.16641

New Quantum and LCD Codes over Finite Fields of Even Characteristic

Habibul Islam Indian Institute of Technology Patna , Patna- India https://orcid.org/0000-0002-2196-1586
Om Prakash Indian Institute of Technology Patna, Patna- India https://orcid.org/0000-0002-6512-4229

DOI: https://doi.org/10.14429/dsj.71.16641

Keywords: Cyclic codes, Gray map, Quantum code, LCD codes

Abstract

For an integer m ≥ 1, we study cyclic codes of length l over a commutative non-chain ring F_2m + uF_2m , where u² = u . With a new Gray map and Euclidean dual-containing cyclic codes, we provide many new and superior codes to the best-known quantum error-correcting codes. Also, we characterise LCD codes of length l with respect to their generator polynomials and prove that F_2m − image of an LCD code of length l is an LCD code of length 2l . Finally, we provide several optimal LCD codes from the Gray images of LCD codes over F_2m + uF_2m .

Published

2021-09-02

How to Cite

Islam, H., & Prakash, O. (2021). New Quantum and LCD Codes over Finite Fields of Even Characteristic. Defence Science Journal, 71(5), 656-661. https://doi.org/10.14429/dsj.71.16641

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Issue

Vol 71 No 5

Section

Computers & Systems Studies

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