328 research outputs found
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
On the equivalence of linear cyclic and constacyclic codes
We introduce new sufficient conditions for permutation and monomial
equivalence of linear cyclic codes over various finite fields. We recall that
monomial equivalence and isometric equivalence are the same relation for linear
codes over finite fields. A necessary and sufficient condition for the monomial
equivalence of linear cyclic codes through a shift map on their defining set is
also given. Moreover, we provide new algebraic criteria for the monomial
equivalence of constacyclic codes over . Finally, we prove that
if , then all permutation equivalent constacyclic codes of
length over are given by the action of multipliers. The
results of this work allow us to prune the search algorithm for new linear
codes and discover record-breaking linear and quantum codes.Comment: 18 page
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
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