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Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 4/2023

27.05.2023 | Original Research

A family of cyclic codes with two zeros

verfasst von: Yunfei Su, Xiaoshan Kai

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 4/2023

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Abstract

Cyclic codes have been applied in communication systems, data storage systems and consumer electronics widely. In this work, we explore q-ary cyclic codes of length \(n=\frac{q^{m}-1}{r}\) having two zeros. For such cyclic codes, a sufficient and necessary condition with minimum distance two is given. It is shown that such cyclic codes have minimum distance at most three when \(q>2r+1\). For \(r=\frac{q-1}{2}\), we obtain an optimal family of cyclic codes with parameters \(\left[ \frac{2\left( q^{m}-1\right) }{q-1},\frac{2\left( q^{m}-1\right) }{q-1}-2m,4\right] \).
Vorheriger Artikel Dynamics and calculation of the basic reproduction number for a nonlocal dispersal epidemic model with air pollution
Nächster Artikel Dynamics of a fractional COVID-19 model with immunity using harmonic incidence mean-type

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Metadaten
Titel
A family of cyclic codes with two zeros
verfasst von
Yunfei Su
Xiaoshan Kai
Publikationsdatum
27.05.2023
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 4/2023
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-023-01876-6

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