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Erschienen in: Designs, Codes and Cryptography 3/2016

01.03.2016

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

verfasst von: Maosheng Xiong, Nian Li, Zhengchun Zhou, Cunsheng Ding

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

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Abstract

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. Most previous results obtained so far were for cyclic codes with no more than three zeroes. Inspired by the works of Li et al. (Sci China Math 53:3279–3286, 2010; IEEE Trans Inf Theory 60:3903–3912, 2014), we study two families of cyclic codes over \({\mathbb F}_p\) with arbitrary number of zeroes of generalized Niho type, more precisely \({\mathcal {C}_{(d_0,d_1,\ldots ,d_t)}^{(1)}}\) (for \(p=2\)) of \(t+1\) zeroes, and \({\mathcal {C}_{(\widetilde{d}_1,\ldots ,\widetilde{d}_t)}^{(2)}}\) (for any prime \(p\)) of \(t\) zeroes for any \(t\). We find that the first family has at most \((2t+1)\) non-zero weights, and the second has at most \(2t\) non-zero weights. Their weight distribution are also determined in the paper.
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Metadaten
Titel
Weight distribution of cyclic codes with arbitrary number of generalized Niho type zeroes
verfasst von
Maosheng Xiong
Nian Li
Zhengchun Zhou
Cunsheng Ding
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/s10623-014-0027-5

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