New Quantum and LCD Codes over Finite Fields of Even Characteristic

Authors

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 F2m + uF2m , 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 F2m − 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 F2m + uF2m .

 

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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

Issue

Vol. 71 No. 5

Section

Computers & Systems Studies

License

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