Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros

Xiaoni Du1,2; Rong Wang1; Chunming Tang3; Qi Wang4

2020

10.3934/amc.2020106

Advances in Mathematics of Communications   影响因子和分区

1930-5346

1930-5338

Combinatorial t-designs have been an interesting topic in combi-natorics for decades. It is a basic fact that the codewords of a fixed weight in a code may hold a t-design. Till now only a small amount of work on constructing t-designs from codes has been done. In this paper, we determine the weight distributions of two classes of cyclic codes: one related to the triple-error correcting binary BCH codes, and the other related to the cyclic codes with parameters satisfying the generalized Kasami case, respectively. We then obtain infinite families of 2-designs from these codes by proving that they are both affine-invariant codes, and explicitly determine their parameters. In par-ticular, the codes derived from the dual of binary BCH codes hold five 3-designs when m = 4.

2-design Affine-invariant code BCH code Cyclic code Linear code Weight distribution

英语

其他

2-s2.0-85101822893

人工提交

1.College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China
2.Guangxi Key Laboratory of Cryptography and Information Security Guilin University of Electronic Technology Guilin, Guangxi 541004, China
3.School of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, China
4.Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China

Xiaoni Du,Rong Wang,Chunming Tang,et al. Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros[J]. Advances in Mathematics of Communications,2020,16(1):157-168.

Xiaoni Du,Rong Wang,Chunming Tang,&Qi Wang.(2020).Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros.Advances in Mathematics of Communications,16(1),157-168.

Xiaoni Du,et al."Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros".Advances in Mathematics of Communications 16.1(2020):157-168.