[图书][B] Graph Algebras and Automata

AV Kelarev - 2003 - books.google.com
Graph algebras possess the capacity to relate fundamental concepts of computer science,
combinatorics, graph theory, operations research, and universal algebra. They are used to …

[图书][B] Ring constructions and applications

AV Kelarev - 2002 - books.google.com
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 …

[图书][B] Finite Fields: Theory and Computation: The meeting point of number theory, computer science, coding theory and cryptography

I Shparlinski - 2013 - books.google.com
This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

[HTML][HTML] Repeated-root cyclic and negacyclic codes over a finite chain ring

A Sălăgean - Discrete applied mathematics, 2006 - Elsevier
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 …

Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes

SR López-Permouth, H Özadam, F Özbudak… - Finite Fields and Their …, 2013 - Elsevier
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 …

[PDF][PDF] Error-correcting codes as ideals in group rings

AV Kelarev, P Solé - Contemporary Mathematics, 2001 - academia.edu
Error-correcting Codes as Ideals in Group Rings Page 1 Contenporary Mathematics Volume
273, 2001 Error-correcting Codes as Ideals in Group Rings AV Kelarev and P. Solé Dedicated …

Multivariable codes over finite chain rings: serial codes

E Martínez-Moro, IF Rúa - SIAM Journal on Discrete Mathematics, 2006 - SIAM
The structure of multivariate serial codes over a finite chain ring R is established using the
structure of the residue field ̄R. Multivariate codes extend in a natural way the univariate …

[PDF][PDF] On finite principal ideal rings

J Cazaran, AV Kelarev - Acta Math. Univ. Comenianae, 1999 - iam.fmph.uniba.sk
77 ON FINITE PRINCIPAL IDEAL RINGS 1. Main Results Finite commutative rings are
interesting objects of ring theory and have many Page 1 Acta Math. Univ. Comenianae Vol …

[HTML][HTML] Encoding through generalized polynomial codes

T Shah, A Khan, AA Andrade - Computational & Applied Mathematics, 2011 - SciELO Brasil
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 …

An algorithm for computing the minimum distances of extensions of BCH codes embedded in semigroup rings

J Cazaran, AV Kelarev, SJ Quinn, D Vertigan - Semigroup Forum, 2006 - Springer
An Algorithm for Computing the Minimum Distances of Extensions of BCH Codes
Embedded in Semigroup Rings Page 1 Semigroup Forum Vol. 73 (2006) 317–329 c 2006 …