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Constacyclic Codes Of Length nps OVER Fpm + uFpm

Authors: 

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

Source title: 
Advances in Mathematics of Communications, 12(2): 231-262, 2018 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

Let Fpm be a finite field of cardinality pm and R=Fpm[u]/⟨u2⟩=Fp+ uFp (u2=0), where p is a prime and m is a positive integer. For any λ ∈ F×pm, an explicit representation for all distinct λ-constacyclic codes over R of length nps is given by a canonical form decomposition for each code, where s and n are arbitrary positive integers satisfying gcd(p,n)=1. For any such code, using its canonical form decomposition the representation for the dual code of the code is provided. Moreover, representations for all distinct cyclic codes, negacyclic codes and their dual codes of length nps over R are obtained, and self-duality for these codes are determined. Finally, all distinct self-dual negacyclic codes over F5+uF5 of length 2⋅3t⋅5s are listed for any positive integer t.