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On constacyclic codes of length 4ps over Fpm + uFpm

Authors: 

Hai Q. Dinh, Sompong Dhompongsa, Songsak Sriboonchitta

Source title: 
Discrete Mathematics, 340(4): 832-849, 2017 (ISI)
Academic year of acceptance: 
2016-2017
Abstract: 

For any odd prime p such that p≡ (mo4), the structures of all λ-constacyclic codes of length 4ps over the finite commutative chain ring Fpm+uFpm (u= 0are established in terms of their generator polynomials. If the unit λ is a square, each λ-constacyclic code of length 4ps  is expressed as a direct sum of an α-constacyclic code and an α-constacyclic code of length 2ps. In the main case that the unit λ is not a square, it is shown that any nonzero polynomial of degree <4 over Fpm is invertible in the ambient ring abstract-bai-anh-Hai-1.1.png . When the unit λ is of the form λ α uβ for nonzero elements α,β of Fpm, it is obtained that the ambient ring abstract-bai-anh-Hai-2.png is a chain ring with maximal ideal x4 − α0, and so the (α uβ)-constacyclic codes are(x− α0)i, for 0i2ps. For the remaining case, that the unit λ is not a square, and λ γ for a nonzero element γ of Fpm , it is proven that the ambient ring abstract-bai-anh-Hai-3.png is a local ring with the unique maximal idealx− γ0,u. Such λ-constacyclic codes are then classified into 4 distinct types of ideals, and the detailed structures of ideals in each type are provided. Among other results, the number of codewords, and the dual of each λ-constacyclic code are provided.