On The Relationship between (16,6,3)-Designs and (25,12) Self-Orthogonal Codes

TL;DR

This paper explores the connection between specific combinatorial designs and self-orthogonal codes, revealing how (16,6,3)-designs are distributed within binary (25,12) self-orthogonal codes and their interrelationships.

Contribution

It establishes the distribution of (16,6,3)-designs in binary (25,12) self-orthogonal codes and analyzes the relationships among codes with embedded designs.

Findings

Distribution of (16,6,3)-designs in codes

Relationships among codes with embedded designs

Insights into the structure of self-orthogonal codes

Abstract

Binary self-orthogonal codes and balanced incomplete block designs are two combinatorial configurations that have been much studied because of their wide areas of application. In this paper, we have shown the distribution of (16; 6; 3)-designs in binary (25,12) self-orthogonal codes. The paper also presents the relationships among the codes with embedded designs.