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

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

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...

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Veröffentlicht in:Axioms 2022-10, Vol.11 (10), p.519
Hauptverfasser: Alabiad, Sami, Alkhamees, Yousef
Format: Artikel
Sprache:eng
Schlagworte:
Binary system
Codes
coding theory
cyclic codes
Fourier transforms
Galois rings
Linear codes
Polynomials
Representations
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Zusammenfassung: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11100519