Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776967 | Discrete Mathematics | 2017 | 18 Pages |
Abstract
For any odd prime p such that pmâ¡1(mod4), the structures of all λ-constacyclic codes of length 4ps over the finite commutative chain ring Fpm+uFpm(u2=0) are 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 âα-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 (Fpm+uFpm)[x]ãx4psâλã. 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 (Fpm+uFpm)[x]ãx4psâ(α+uβ)ã is a chain ring with maximal ideal ãx4âα0ã, and so the (α+uβ)-constacyclic codes are ã(x4âα0)iã, for 0â¤iâ¤2ps. 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 (Fpm+uFpm)[x]ãx4psâγã is a local ring with the unique maximal ideal ãx4âγ0,uã. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Hai Q. Dinh, Sompong Dhompongsa, Songsak Sriboonchitta,