[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 …
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 …
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 …
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 …
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
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 …
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 …
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 …
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 …
interesting objects of ring theory and have many Page 1 Acta Math. Univ. Comenianae Vol …
[HTML][HTML] Encoding through generalized polynomial codes
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 …
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
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 …
Embedded in Semigroup Rings Page 1 Semigroup Forum Vol. 73 (2006) 317–329 c 2006 …