37 research outputs found
Some Constacyclic Codes over Finite Chain Rings
For an -th power of a unit in a finite chain ring we prove that
-constacyclic repeated-root codes over some finite chain rings are
equivalent to cyclic codes. This allows us to simplify the structure of some
constacylic codes. We also study the -constacyclic codes of
length over the Galois ring
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 polynomial ring. The structure of the ambient ring of
polycyclic codes over GR(p^a,m) and generating sets for its ideals are
considered. Along with some structure details of the ambient ring, the
existance of a certain type of generating set for an ideal is proven.Comment: arXiv admin note: text overlap with arXiv:0906.400
Repeated-root cyclic and negacyclic codes over a finite chain ring
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 ring with characteristic a power of 2. For any other finite chain ring
they are in general not principally generated. We also prove results on the structure,
cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a
finite chain ring
Repeated-root cyclic and negacyclic codes over a finite chain ring
AbstractWe 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 ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring
Repeated-root cyclic and negacyclic codes over a finite chain ring
AbstractWe 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 ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring
Multivariable codes in principal ideal polynomial quotient rings with applications to additive modular bivariate codes over F4
Producción CientÃficaIn this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field F4Ministerio de EconomÃa, Industria y Competitividad (MTM2013-45588-C3-1-P / MTM2015-65764-C3-1-P / MTM2015-69138-REDT)Principado de Asturias (GRUPIN14-142
Constacyclic Codes over Finite Fields
An equivalence relation called isometry is introduced to classify
constacyclic codes over a finite field; the polynomial generators of
constacyclic codes of length are characterized, where is the
characteristic of the finite field and is a prime different from