In this article, we study skew cyclic codes over ring R = Fq + vFq + v 2 Fq, where q = p, p is an odd prime and v3 = v. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomials of the duals of skew cyclic codes. Moreover, the idempotent genera...

In network coding, a flag code is set of sequences nested subspaces $${{\mathbb {F}}}_q^n$$ , being {F}}}_q$$ the finite field with q elements. Flag codes defined as orbits cyclic subgroup general linear group acting on flags are called orbit codes. Inspired by ideas in Gluesing-Luerssen et al. (Adv Math Commun 9(2):177–197, 2015), we determine cardinality and provide bounds for its distance he...

We study the codes of title by CRT method, that decomposes such into constituent codes, which are shorter over larger alphabets. Criteria on these for self-duality and linear complementary duality decomposed derived. The special class one-generator is given a polynomial representation exactly enumerated. In particular, we present some illustrative examples binary optimal with respect to Griesme...

In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R = Z3+vZ3+v 2 Z3, v 3 = v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasicyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The paramete...

General isometries of cyclic codes, including multipliers and translations, are introduced; and isometrically self-dual cyclic codes are defined. In terms of Type-I duadic splittings given by multipliers and translations, a necessary and sufficient condition for the existence of isometrically selfdual cyclic codes is obtained. A program to construct isometrically selfdual cyclic codes is provid...

This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descenda...