Pseudo Quasi-3 Designs and their Applications to Coding Theory

TL;DR

This paper introduces pseudo quasi-3 designs, a new class of symmetric designs, and demonstrates their application in constructing optimal self-complementary codes that meet the Grey Rankin bound.

Contribution

It provides a novel construction of an infinite family of pseudo quasi-3 designs and links them to the development of codes with optimal parameters.

Findings

Constructed an infinite family of pseudo quasi-3 designs.

Enabled the creation of codes meeting the Grey Rankin bound.

Linked design theory with optimal coding solutions.

Abstract

We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmetric designs can be used to construct optimal self complementary codes. In this article we give a construction of an infinite family of pseudo quasi-3 designs whose residual designs allow us to construct a family of codes with a new parameter set that meet the Grey Rankin bound.