A class of repeated-root constacyclic codes over 𝔽pm [u]/〈ue〉 of Type 2
A class of repeated-root constacyclic codes over 𝔽pm [u]/〈ue〉 of Type 2
Source title:
Finite Fields and Their Applications, 55: 238-267,
2019
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
Let be a finite field of cardinality
where p is an odd prime, n be a positive integer satisfying
, and denote
where
be an even integer. Let
. Then the class of
constacyclic codes over R is a significant subclass of constacyclic codes over R of Type 2. For any integer
, an explicit representation and a complete description for all distinct
constacyclic codes over R of length npk and their dual codes are given. Moreover, formulas for the number of codewords in each code and the number of all such codes are provided respectively. In particular, all distinct
constacyclic codes over
of length pk and their dual codes are presented precisely.