Results 1 to 10 of about 43 (42)

Symbol-Triple Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over ${\mathbb{F}}_q+u{\mathbb{F}}_q+u^2{\mathbb{F}}_q$

Mathematics, 2022
Let p be an odd prime, where ϑ and m are positive integers. Let ψ be a nonzero element of the finite field Fq, where q=pm, and R=Fq+uFq+u2Fq(u3=0). In this paper, we determine completely the symbol-triple distances of all ψ-constacyclic codes of length ...
Hai Q. Dinh, Jamal Laaouine, Brahim Boudine, Woraphon Yamaka   +3 more
doaj   +1 more source

Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\)

Mathematics, 2021
Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring.
Mohammed E. Charkani, Hai Q. Dinh, Jamal Laaouine, Woraphon Yamaka   +3 more
doaj   +1 more source

Repeated-Root Constacyclic Codes Over the Chain Ring F_p^m[u]/⟨u³⟩

IEEE Access, 2020
Let Z = Fpm[u]/(u3) be the finite commutative chain ring, where p is a prime, m is a positive integer and Fpm is the finite field with pm elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over Z and their ...
Tania Sidana, Anuradha Sharma
doaj   +1 more source

Quantum MDS and Synchronizable Codes From Cyclic and Negacyclic Codes of Length 2p^s Over F_p^m

IEEE Access, 2020
Let p be an odd prime, and Fp(m) is the finite field of pm elements. In this paper, all maximum distance separable (briefly, MDS) cyclic and negacyclic codes of length 2ps over Fp(m) are established.
Hai Q. Dinh, Bac T Nguyen, Woraphon Yamaka   +2 more
doaj   +1 more source

Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications

Journal of Mathematics, 2022
Cyclic codes play a very important role in the history of coding theory since they have good algebraic structures that can be widely used in coding and decoding.
Hongju Li, Ping Yu, Jing Liang, Feng Zhao   +3 more
doaj   +1 more source

Some Classes of New Quantum MDS and Synchronizable Codes Constructed From Repeated-Root Cyclic Codes of Length 6p^s

IEEE Access, 2021
In this paper, we use the CSS and Steane’s constructions to establish quantum error-correcting codes (briefly, QEC codes) from cyclic codes of length $6p^{s}$ over $\mathbb F_{p^{m}}$ .
Hai Q. Dinh, Ha T. Le, Bac T. Nguyen, Paravee Maneejuk   +3 more
doaj   +1 more source

On a Family of Quantum Synchronizable Codes Based on the $(\lambda(u + v)|u - v)$ Construction

IEEE Access, 2020
In this paper, we propose a family of quantum synchronizable codes from repeated-root cyclic codes and constacyclic codes. This family of quantum synchronizable codes are based on (λ(u + v)|u - v) construction which is constructed from ...
Chao Du, Zhi Ma, Lan Luo, Dakang Huang, Hong Wang   +4 more
doaj   +1 more source

Constacyclic Codes of Length 3p^s Over F_p^m + uF_p^m and Their Application in Various Distance Distributions

IEEE Access, 2020
Let p ≠ 3 be any prime. The structures of all λ-constacyclic codes of length 3ps over the finite commutative chain ring Fpm + uFpm (u2 = 0) are established in the term of their generator polynomials.
Hai Q. Dinh, Bac Trong Nguyen, Woraphon Yamaka   +2 more
doaj   +1 more source

On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6p^s

IEEE Access, 2020
Let $p$ be an odd prime, $s$ , $m$ be positive integers such that $p^{m}\equiv 2 \pmod 3$ . In this paper, using the relationship about Hamming distances between simple-root cyclic codes and repeated-root cyclic codes, the Hamming distance of all ...
Hai Q. Dinh, Xiaoqiang Wang, Paravee Maneejuk   +2 more
doaj   +1 more source

On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5p^s Over F_p ^m + uF_p ^m

IEEE Access, 2022
Let $p\not =5$ be any odd prime. Using the algebraic structures of all cyclic codes of length $5p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , in this paper, the exact values of Hamming ...
Hai Q. Dinh, Bac T. Nguyen, Hiep L. Thi, Woraphon Yamaka   +3 more
doaj   +1 more source