2019/04/05 by Chunming Tang, Tang, Chunming
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1904.04071
openalex publication_date 2019/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Combinatorial t-designs have nice applications in coding theory, finite geometries and several engineering areas. The objective of this paper is to study how to obtain 3-designs with 2-transitive permutation groups. The incidence structure formed by the orbits of a base block under the action of the general affine groups, which are 2-transitive, is considered. A characterization of such incidence structure to be a 3-design is presented, and a sufficient condition for the stabilizer of a base block to be trivial is given. With these general results, infinite families of 3-designs are constructed by employing APN functions. Some 3-designs presented in this paper give rise to self-dual binary codes or linear codes with optimal or best parameters known. Several conjectures on 3-designs and binary codes are also presented.