2016/07/17 by Cunsheng Ding, Ding, Cunsheng
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #graph theory and CDMA systems #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.1607.04815
It has been known for a long time that t-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a t-design. While a lot of progress in the direction of constructing codes from t-designs has been made, only a small amount of work on the construction of t-designs from codes has been done. The objective of this paper is to construct infinite families of 2-designs and 3-designs from a type of binary linear codes with five-weights. The total number of 2-designs and 3-designs obtained in this paper are exponential in any odd m and the block size of the designs varies in a huge range.