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

Content Provider	Springer Nature Link
Author	Ding, Cunsheng Xiong, Maosheng Li, Nian Zhou, Zhengchun
Copyright Year	2014
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.
Ending Page	730
Page Count	18
Starting Page	713
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	3
Volume Number	78
Language	English
Publisher	Springer US
Publisher Date	2014-12-02
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Weight distribution Information and Communication, Circuits Data Structures, Cryptology and Information Theory Trigonometric and exponential sums, general Niho exponent Discrete Mathematics in Computer Science Data Encryption Algebraic coding theory; cryptography Coding and Information Theory Combinatorics Cyclic codes Vandermonde matrix
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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