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Infinite families of 2-designs from a class of non-binary Kasami cyclic codes

Rong Wang, ,College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China, Xiaoni Du, Cuiling Fan, ,Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China, ,School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610000, China
2019 Advances in Mathematics of Communications  

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Combinatorial t-designs have been an important research subject for many years, as they have wide applications in coding theory, cryptography, communications and statistics. The interplay between coding theory and tdesigns has been attracted a lot of attention for both directions. It is well known that a linear code over any finite field can be derived from the incidence matrix of a t-design, meanwhile, that the supports of all codewords with a fixed weight in a code also may hold a t-design.
more » ... this paper, by determining the weight distribution of a class of linear codes derived from non-binary Kasami cyclic codes, we obtain infinite families of 2-designs from the supports of all codewords with a fixed weight in these codes, and calculate their parameters explicitly. 2020 Mathematics Subject Classification: Primary: 05B05, 94B05, 11T23, 11T71.
doi:10.3934/amc.2020088 fatcat:uqgxecvpvzaudfquh3fesy6oa4
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Rong Wang, ,College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China, Xiaoni Du, Cuiling Fan, ,Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China, ,School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610000, China. "Infinite families of 2-designs from a class of non-binary Kasami cyclic codes." Advances in Mathematics of Communications 15.4 (2019) 0-0