Graph algebras possess the capacity to relate fundamental concepts of computer science,
combinatorics, graph theory, operations research, and universal algebra. They are used to …

This book contains the definitions of several ring constructions used in various applications.
The concept of a groupoid-graded ring includes many of these constructions as special …

We show that repeated-root cyclic codes over a finite chain ring are in general not principally
generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois …

Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called
polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a …

In this paper, we investigate the algebraic structure for polycyclic codes over a specific class
of serial rings, defined as R= R [x 1,…, xs]/⟨ t 1 (x 1),…, ts (xs)⟩, where R is a chain ring and …

This paper introduces novel constructions of cyclic codes using semigroup rings instead of
polynomial rings. These constructions are applied to define and investigate the BCH …

A notion of a balanced automorphism of a group was introduced in Sirǎn and Skoviera
(1992) in order to study regular Cayley maps over finite groups. One of the open questions …

For any finite commutative ring B with an identity there is a strict inclusion B [X; Z0]⊂ B [X;
12; Z0]⊂ B [X; 122Z0] of commutative semigroup rings. This work is a continuation of Shah …

In this work we consider repeated-root multivariable codes over a finite chain ring. We show
conditions for these codes to be principally generated. We consider a suitable set of …

In this paper, a transform approach is used for polycyclic and serial codes over finite local
rings in the case that the defining polynomials have no multiple roots. This allows us to study …