Symmetric Designs and Self-Dual Codes over Rings

Abstract

We describe a technique for producing self-dual codes over rings and fields from symmetric designs. We give special attention to biplanes and determine the minimum weights of the codes formed from these designs. We give numerous examples of self-dual codes constructed including an optimal code of length \(22\) over \(\mathbb{Z}_4\) with respect to the Hamming metric from the biplane of order \(3\).