Journal of Science and Technology

URI vĩnh viễn cho bộ sưu tập này

https://oerrepository.ntt.edu.vn/handle/298300331/3

Duyệt qua

Đang duyệt Journal of Science and Technology theo Chủ đề

Đang hiển thị 1 - 2 trong tổng số 2
  • Hình ảnh thu nhỏ
    Tài liệu
    On (α + uβ)-constacyclic codes of length 4ps over Fpm+ uFpm
    (Trường Đại học Nguyễn Tất Thành, 2018-03-26) Q. Hai Dinh; Nguyen. T Bac; Songsak Sriboonchitta
    Present for any odd prime p such that pm ≡ 3 (mod 4), the structures of all (α + uβ)- constacyclic codes of length 4ps over the finite commutative chain ring Fpm + uFpm (u2 = 0) are established in term of their generator polynomials. When the unit (α+ uβ) is a square, each (α + uβ)-constacyclic code of length 4ps is expressed as a direct sum of two constacyclic codes of length 2ps. In the main case that the unit (α + uβ) is not a square, it is shown that the ambient ring (Fpm +uFpm )[x]∗x4ps −(α+uβ) is a principal ideal ring. From that, the structure, number of codewords, duals of all such (α + uβ)-constacyclic codes are obtained. As an application, we identify all self-orthogonal, dual-containing, and the unique self-dual (α + uβ)-constacyclic codes of length 4ps over Fpm + uFpm
  • Hình ảnh thu nhỏ
    Tài liệu
    On a class of constacyclic codes of length 4ps over Fpm + uFpm
    (World Scientific Publishing Company DOI, 2017-12-24) Hai Q. Dinh; Bac T. Nguyen; Songsak Sriboonchitta
    Present Let p be a prime such that pm ≡3 (mod 4). For any unit λ of Fpm , we determine the algebraic structures of λ-constacyclic codes of length 4ps over the finite commutative chain ring Fpm + uFpm , u2 = 0. If the unit λ ∈ Fpm is a square, each λ-constacycliccode of length 4ps is expressed as a direct sum of an -α-constacyclic code and an α constacyclic code of length 2ps. If the unit λ is not a square, then x4 −λ0 can bedecomposed into a product of two irreducible coprime quadratic polynomials which arex2 + γx + γ2 2 and x 2 −γx + γ2 2 , where λ ps 0 = λ and γ4 = −4λ0. By showing that thequotient rings ˙` R x2+γx+γ2 2 ´ps ¸ and nR˙`x2−γx+γ2 2 ´ps ¸ are local, non-chain rings, we can compute the number of codewords in each of λ-constacyclic codes. Moreover, the duals of such codes are also given.