Infinite families of cyclic and negacyclic codes supporting 3-designs
(2207.07262)Abstract
Interplay between coding theory and combinatorial $t$-designs has been a hot topic for many years for combinatorialists and coding theorists. Some infinite families of cyclic codes supporting infinite families of $3$-designs have been constructed in the past 50 years. However, no infinite family of negacyclic codes supporting an infinite family of $3$-designs has been reported in the literature. This is the main motivation of this paper. Let $q=pm$, where $p$ is an odd prime and $m \geq 2$ is an integer. The objective of this paper is to present an infinite family of cyclic codes over $\gf(q)$ supporting an infinite family of $3$-designs and two infinite families of negacyclic codes over $\gf(q2)$ supporting two infinite families of $3$-designs. The parameters and the weight distributions of these codes are determined. The subfield subcodes of these negacyclic codes over $\gf(q)$ are studied. Three infinite families of almost MDS codes are also presented. A constacyclic code over GF($4$) supporting a $4$-design and six open problems are also presented in this paper.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.