Infinite families of 2-designs and 3-designs from linear codes

Abstract

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.

References in corpus (2)

• Narrow-Sense BCH Codes over $\gf(q)$ with Length $n=\frac{q^m-1}{q-1}$
• The Dimension and Minimum Distance of Two Classes of Primitive BCH Codes

Cited by in corpus (3)

• Narrow-Sense BCH Codes over $\gf(q)$ with Length $n=\frac{q^m-1}{q-1}$
• Weighted Subspace Designs from $q$-Polymatroids
• An infinite family of Steiner systems $S(2,4,2^m)$ from cyclic codes