English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Interplay between coding theory and combinatorial $t$-designs has been a hottopic for many years for combinatorialists and coding theorists. Some infinitefamilies of cyclic codes supporting infinite families of $3$-designs have beenconstructed in the past 50 years. However, no infinite family of negacycliccodes supporting an infinite family of $3$-designs has been reported in theliterature. This is the main motivation of this paper. Let $q=p^m$, where $p$is an odd prime and $m \geq 2$ is an integer. The objective of this paper is topresent an infinite family of cyclic codes over $\gf(q)$ supporting an infinitefamily of $3$-designs and two infinite families of negacyclic codes over$\gf(q^2)$ supporting two infinite families of $3$-designs. The parameters andthe weight distributions of these codes are determined. The subfield subcodesof these negacyclic codes over $\gf(q)$ are studied. Three infinite families ofalmost 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.

Infinite families of cyclic and negacyclic codes supporting 3-designs