Self-orthogonal and self-dual codes constructed via combinatorial designs and Diophantine equations
A self-dual code over \(\mathbb{Z}_p\) is a subcode \(C\) of \(\mathbb{Z}_p^n\) with \(C=C^\perp.\) These codes are of great interest from a coding theory perspective and also with respect to their connection with finite designs. Numerous constructions of these codes from combinatorial structures exist in the literature. Orthogonal designs and generalized orthogonal designs can be described as matrices satisfying certain algebraic conditions. In this work the authors generalize some constructions using orthogonal designs, generalized orthogonal designs and Diophantine equations to construct new self-dual and self-orthogonal codes. They construct new self-dual codes of length \(32\) over \(\mathbb{Z}_{11}\) and \(\mathbb{Z}_{13}\) with minimum distance \(12\) which are better than previously known codes for these cases.
scientific article; zbMATH DE number 2091515