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Designs, Codes and Cryptography

Erschienen in:

01.03.2016

The weight distribution of a family of \(p\)-ary cyclic codes

verfasst von: Long Yu, Hongwei Liu

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2016

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Abstract

Let \(m\), \(k\) be positive integers, \(p\) be an odd prime and \(\pi \) be a primitive element of \({\mathbb {F}}_{p^m}\). In this paper, we determine the weight distribution of a family of cyclic codes \({\mathcal {C}}_t\) over \({\mathbb {F}}_p\), whose duals have two zeros \(\pi ^{-t}\) and \(-\pi ^{-t}\), where \(t\) satisfies \(t\equiv \frac{p^k+1}{2}p^\tau \ (\mathrm{mod}\ \frac{p^m-1}{2}) \) for some \(\tau \in \{0,1,\ldots , m-1\}\).

Vorheriger Artikel Weight distribution of cyclic codes with arbitrary number of generalized Niho type zeroes

Nächster Artikel Optimal equi-difference conflict-avoiding codes of weight four

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Titel: The weight distribution of a family of -ary cyclic codes
verfasst von: Long Yu
Hongwei Liu
Publikationsdatum: 01.03.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-014-0029-3

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