Article in press
Authors:
Title:
Some LCD cyclic codes of length 2p over finite fields
PDFSource:
Discussiones Mathematicae - General Algebra and Applications
Received: 2022-09-08 , Revised: 2023-01-10 , Accepted: 2023-01-10 , Available online: 2023-11-15 , https://doi.org/10.7151/dmgaa.1447
Abstract:
In this paper, we explicitly determine the $LCD$ minimal and maximal cyclic
codes of length $2p$ over finite fields $\mathbb{F}_{q}$ with $p$ and $q$
are distinct odd primes and $\phi (p)=p-1$ is the multiplicative order of $q$
modulo $2p.$ We show that, every $LCD$ maximal cyclic code is a direct sum
of $LCD$ minimal cyclic codes.
Primary keywords:
linear and cyclic codes
Secondary keywords:
LCD codes, reversible codes.
References:
- S.K. Arora and M. Pruthi, Minimal cyclic codes of length $2p^{n}$, Finite Fields Appl. 5 (1999) 177–187.\newline https://doi.org/10.1006/ffta.1998.0238
- S. Batra and S. K. Arora, Some cyclic codes of length $ 2p^{n}$, Des. Codes Cryptogr. 61(1), 41–69 (2011).\newline https://doi.org/10.1007/s10623-010-9438-0
- W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, Cambridge, 2003.\newline
- R. Lidl and G. Pilz, Applied Abstract Algebra, Springer -Verlag. Ney York, 1998.\newline
- S. Ling and C. xing, Coding Theory, A First Course, Cambridge University Press, 2004.\newline
- C. Li, C. Ding and S. Li, $LCD$\ cyclic codes over finite fields, IEEE Trans. Inf. Theory 63 (2017) 4344–4356.\newline https://doi.org/10.1109/TIT.2017.2672961
- J. L and Massey, Reversible codes, Information and Control, 7 (1964), 369-380.\newline https://doi.org/10.1016/S0019-9958(64)90438-3
- J. L and Massey, Linear codes with complementary duals, Discrete Math. 106/107 (1992) 337–342.\newline https://doi.org/10.1016/0012-365X(92)90563-U
- V. Pless, Introduction to the Theory of Error Correcting Codes, Wiley, New York, 1998.\newline
- M. Pruthi and S. K. Arora, Minimal cyclic codes of prime power length, Finite Fields Appl. 3 (1997) 99–113.\newline https://doi.org/10.1006/ffta.1998.0238
- X. Yang and J. L. Massey, The condition for a cyclic code to have a complementary dual, Discrete Math. 126 (1994) 391–393. \newline https://doi.org/10.1016/0012-365X(94)90283-6
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