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Zhu, Shixin; Kai, Xiaoshan

doi:10.1016/j.disc.2008.05.013

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Discrete Fourier Transform (Dft)1

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Cited by 17 publications

(1 citation statement)

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“…Discrete Fourier transform (DFT) is used when the codes length, N, is an arbitrary number not necessarily a power of primes; in our case, N = n 1 p s and (n 1 , p) = 1. This method has been widely utilized to investigate linear codes over finite rings, for instance see [1,4,5,12,23,24]. Next, we use DFT as an important key to describe the structure for cyclic codes over GR(p n , r).…”

Section: Discrete Fourier Transform (Dft)mentioning

confidence: 99%

A Unique Representation of Cyclic Codes over GR(pn,r)

Alabiad¹,

Alkhamees²

2022

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Let R be a Galois ring, GR(pn,r), of characteristic pn and of order pnr. In this article, we study cyclic codes of arbitrary length, N, over R. We use discrete Fourier transform (DFT) to determine a unique representation of cyclic codes of length, N, in terms of that of length, ps, where s=vp(N) and vp are the p-adic valuation. As a result, Hamming distance and dual codes are obtained. In addition, we compute the exact number of distinct cyclic codes over R when n=2.

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Section: Discrete Fourier Transform (Dft)mentioning

confidence: 99%

A Unique Representation of Cyclic Codes over GR(pn,r)

Alabiad¹,

Alkhamees²

2022

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Negacyclic self-dual codes over finite chain rings

Kai

Zhu

2011

Des. Codes Cryptogr.

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In this article, we study negacyclic self-dual codes of length n over a finite chain ring R when the characteristic p of the residue fieldR and the length n are relatively prime. We give necessary and sufficient conditions for the existence of (nontrivial) negacyclic selfdual codes over a finite chain ring. As an application, we construct negacyclic MDR self-dual codes over GR(p t , m) of length p m + 1.

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On Constacyclic Codes over $$\boldsymbol{Z}_{\boldsymbol{p}_{1}\boldsymbol{p}_{2}\cdots\boldsymbol{p}_{\boldsymbol{t}}}$$

Xie

Liao

2019

Chin. Ann. Math. Ser. B

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Dual and self-dual negacyclic codes of even length over Z2a

Cited by 17 publications

References 19 publications

A Unique Representation of Cyclic Codes over GR(pn,r)

A Unique Representation of Cyclic Codes over GR(pn,r)

Negacyclic self-dual codes over finite chain rings

On Constacyclic Codes over $$\boldsymbol{Z}_{\boldsymbol{p}_{1}\boldsymbol{p}_{2}\cdots\boldsymbol{p}_{\boldsymbol{t}}}$$

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