Construction of reversible cyclic codes over ℤpk

Islam, Habibul; Prakash, Om

doi:10.1080/09720529.2020.1815341

Cited by 3 publications

(2 citation statements)

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“…By using Teorem 16, we see that C is an MHDR cyclic code over R. Also, C is an MDS code, since it is principally generated by a monic polynomial and |Tor 0 (C)| � 5 � |Z 5 | n− d H (Tor 0 (C))+1 (using Teorem 13). 4 , so we see that C is an MDS code over R by using Teorem 13. Also, from Teorem 15, we see that C is also an MHDR code.…”

Section: Theorem 12mentioning

confidence: 88%

“…Cyclic codes over fnite chain rings with length coprime to the characteristic of residue feld have been investigated in references [2,16,22]. Islam and Prakash have established a unique set of generators for cyclic codes over Z p k in reference [4] and for cyclic codes over F q + uF q , u 2 � 0 in reference [5]. A. Sharma and T. Sidana have studied cyclic codes of p s length over fnite chain rings in reference [15], thereby extending the results of Kiah et al on cyclic codes over Galois rings [14].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

MDS and MHDR Cyclic Codes over Finite Chain Rings

Dalal,

Dutt,

Sehmi

2024

Journal of Mathematics

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This work establishes a unique set of generators for a cyclic code over a finite chain ring. Towards this, we first determine the minimal spanning set and rank of the code. Furthermore, sufficient as well as necessary conditions for a cyclic code to be an MDS code and for a cyclic code to be an MHDR code are obtained. Finally, to support our results, some examples of optimal cyclic codes are presented.

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Section: Theorem 12mentioning

confidence: 88%