49 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
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
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