Two-dimensional cyclic codes over a finite chain ring

Two-dimensional cyclic codes over a finite chain ring

In this paper, we have determined the generators and rank of a 2D cyclic code of length over a finite chain ring R with residue field F , where m is arbitrary and ≡ 1( ). Further, we have obtained a necessary and sufficient condition for a 2D cyclic code over a finite chain ring R to be MHDR. Some e...

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Veröffentlicht in:Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică 2024-10, Vol.32 (3), p.75-88
Hauptverfasser: Garg, Disha, Dutt, Sucheta
Format: Artikel
Sprache:eng
Schlagworte:
2D codes
Cyclic codes
Finite chain ring
Hamming distance
Primary 94B15
Secondary 94B05
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Zusammenfassung:In this paper, we have determined the generators and rank of a 2D cyclic code of length over a finite chain ring R with residue field F , where m is arbitrary and ≡ 1( ). Further, we have obtained a necessary and sufficient condition for a 2D cyclic code over a finite chain ring R to be MHDR. Some examples of 2D cyclic codes have been constructed and ranks of these 2D cyclic codes have been calculated by us. We have also given a few examples of 2D cyclic codes over some finite chain rings, which are MHDR.
ISSN:1844-0835
DOI:10.2478/auom-2024-0029