2016/07/17 by Cunsheng Ding, Ding, Cunsheng, Chengju Li +1
Computer Science · Engineering · Mathematics · #05B05 #51E10 #94B15 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1607.04813
openalex publication_date 2016/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The interplay between coding theory and t-designs started many years ago. While every t-design yields a linear code over every finite field, the largest t for which an infinite family of t-designs is derived directly from a linear or nonlinear code is t=3. Sporadic 4-designs and 5-designs were derived from some linear codes of certain parameters. The major objective of this paper is to construct many infinite families of 2-designs and 3-designs from linear codes. The parameters of some known t-designs are also derived. In addition, many conjectured infinite families of 2-designs are also presented.