Type 2 constacyclic codes over 𝔽2m [u]/⟨u3⟩ of oddly even length
Type 2 constacyclic codes over 𝔽2m [u]/⟨u3⟩ of oddly even length
Source title:
Discrete Mathematics, 342(2): 412-426,
2019
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
Let be a finite field of cardinality
be an odd positive integer, and denote
. Let
. Then
constacyclic codes over are called constacyclic codes over of Type 2. In this paper, an explicit representation and a complete description for all distinct
constacyclic codes over of length and their dual codes are given. Moreover, explicit formulas for the number of codewords in each code and the number of all such codes are provided respectively. In particular, all distinct self-dual
constacyclic codes over
of length
are presented precisely. In addition, a complement to a result in Cao et al. (2017) is given.