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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 6/2020

09-03-2020

Linear codes with few weights from cyclotomic classes and weakly regular bent functions

Authors: Yanan Wu, Nian Li, Xiangyong Zeng

Published in: Designs, Codes and Cryptography | Issue 6/2020

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Abstract

Linear codes with few weights constructed from defining sets have been extensively studied due to their applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Li et al. (Appl Algebra Eng Commun Comput 28(1):11–30, 2017) and Jian et al. (Finite Fields Appl 57:92–107, 2019), we propose a class of five-weight linear codes by choosing the defining set from cyclotomic classes, which includes a class of two-weight linear codes as a special case, and we also present two classes of two or three-weight linear codes by employing weakly regular bent functions. Besides, we obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound.
previous article Block transitive codes attaining the Tsfasman–Vladut–Zink bound
next article Relative generalized Hamming weights of affine Cartesian codes
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Metadata
Title
Linear codes with few weights from cyclotomic classes and weakly regular bent functions
Authors
Yanan Wu
Nian Li
Xiangyong Zeng
Publication date
09-03-2020
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 6/2020
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-020-00744-9

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