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Type 2 constacyclic codes over 𝔽2[u]/⟨u3⟩ of oddly even length

Authors: 

Yuan Cao, Yonglin Cao, Hai Q. Dinh, Fang-Wei Fu, Yun Gao, Songsak Sriboonchitta

Source title: 
Discrete Mathematics, 342(2): 412-426, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

Let 22_QuangHai.png be a finite field of cardinality 15_QuangHai.png be an odd positive integer, and denote 16_QuangHai.png. Let 17_QuangHai.png. Then 18_QuangHai.png constacyclic codes over  are called constacyclic codes over  of Type 2. In this paper, an explicit representation and a complete description for all distinct 18_QuangHai.png 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 21_QuangHai.pngconstacyclic codes over 19_QuangHai.png of length 20_QuangHai.png are presented precisely. In addition, a complement to a result in Cao et al. (2017) is given.