Self-dual codes over a family of local rings
A \([n,k,d]_q\) code \(C\) is said to be self-dual if it coincides with its orthogonal space, i.e. \(C=C^\perp\). Self-dual codes possess many interesting properties and are closely related to many other mathematical structures. For example, they have connections to groups, designs, lattices and other mathematical objects as well. For this reason, investigation of classes of codes that are self-dual is an important area of study in coding theory. In this paper the authors, generalizing some previous works, construct a family of commutative rings \(R_{q,\Delta}\). After that, they investigate both the structure of these rings and the codes constructed in \(R_{q,\Delta}\). They determine the parameters that provide the existence of self-dual codes exist and give various constructions of them.
scientific article; zbMATH DE number 7377724