Some Results for Double Cyclic Codes over F[sub.q]+vF[sub.q]+v[sup.2]F[sub.q]

Let F[sub.q] be a finite field with an odd characteristic. In this paper, we present a new result about double cyclic codes over a finite non-chain ring. Specifically, we study the double cyclic code over F[sub.q]+vF[sub.q]+v[sup.2]F[sub.q] with v[sup.3]=v, which is isomorphic to F[sub.q]×F[sub.q]×F...

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Published in:Entropy (Basel, Switzerland) Switzerland), 2024-09, Vol.26 (9)
Main Authors: Deng, Tenghui, Yang, Jing
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Error-correcting codes
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description Let F[sub.q] be a finite field with an odd characteristic. In this paper, we present a new result about double cyclic codes over a finite non-chain ring. Specifically, we study the double cyclic code over F[sub.q]+vF[sub.q]+v[sup.2]F[sub.q] with v[sup.3]=v, which is isomorphic to F[sub.q]×F[sub.q]×F[sub.q]. This study mainly involves generator polynomials and generator matrices. The generating polynomial of the dual code is also obtained. We show the relationship between the generating polynomials of the double cyclic codes and those of their dual codes. Finally, as an application of these results, we construct some optimal codes over F[sub.3].
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title Some Results for Double Cyclic Codes over F[sub.q]+vF[sub.q]+v[sup.2]F[sub.q]
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