Infinite families of 2-designs from a class of affine-invariant codes | Zendy

Yan Liu | Zendy; Xiwang Cao | Zendy

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Infinite families of 2-designs from a class of affine-invariant codes

Author(s) -

Yan Liu,

Xiwang Cao

Publication year - 2022

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2022011

Subject(s) - mathematics , affine transformation , invariant (physics) , linear code , discrete mathematics , class (philosophy) , affine combination , weight distribution , affine hull , combinatorics , pure mathematics , block code , affine space , algorithm , decoding methods , computer science , artificial intelligence , engineering , mathematical physics , aerospace engineering

In this paper, we first introduce a class of cyclic codes and their related linear codes which are affine-invariant. Then we obtain infinite families of 2-designs from the affine-invariant codes. And the parameters of the 2-designs are determined by considering the weight distribution of the linear codes.

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