Article in volume
Authors:
Title:
Some $LCD$ cyclic codes of length $2p$ over finite fields
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 44(2) (2024) 249-259
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.
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