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A class of repeated-root constacyclic codes over 𝔽p[u]/〈ue〉 of Type 2

Authors: 

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

Source title: 
Finite Fields and Their Applications, 55: 238-267, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

Let 7_QuangHai.png be a finite field of cardinality 23_QuangHai.png where p is an odd prime, n be a positive integer satisfying 24_QuangHai.png, and denote 16_QuangHai.png where 26_QuangHai.png be an even integer. Let 27_QuangHai.png. Then the class of 18_QuangHai.pngconstacyclic codes over R is a significant subclass of constacyclic codes over R of Type 2. For any integer 28_QuangHai.png, an explicit representation and a complete description for all distinct 18_QuangHai.pngconstacyclic 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 18_QuangHai.pngconstacyclic codes over 29_QuangHai.png of length pk and their dual codes are presented precisely.