Results 11 to 20 of about 1,045 (128)

Polyadic Constacyclic Codes [PDF]

IEEE Transactions on Information Theory, 2014
For any given positive integer $m$, a necessary and sufficient condition for the existence of Type I $m$-adic constacyclic codes is given. Further, for any given integer $s$, a necessary and sufficient condition for $s$ to be a multiplier of a Type I ...
Chen, Bocong, Dinh, Hai Q., Fan, Yun, Ling, San   +3 more
core   +3 more sources

Application of Constacyclic codes to Quantum MDS Codes [PDF]

IEEE Transactions on Information Theory, 2014
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian construction ...
Chen, Bocong, Ling, San, Zhang, Guanghui
core   +3 more sources

Quantum Codes as an Application of Constacyclic Codes

Axioms
The main focus of this paper is to analyze the algebraic structure of constacyclic codes over the ring R=Fp+w1Fp+w2Fp+w22Fp+w1w2Fp+w1w22Fp, where w12−α2=0, w1w2=w2w1, w23−β2w2=0, and α,β∈Fp∖{0}, for a prime p.
Mohd Arif Raza, Mohammad Fareed Ahmad, Adel Alahmadi, Widyan Basaffar, Manish K. Gupta, Nadeem ur Rehman, Abdul Nadim Khan, Hatoon Shoaib, Patrick Sole   +8 more
doaj   +2 more sources

Quantum Codes Obtained From Constacyclic Codes Over a Family of Finite Rings F_p[u₁, u₂, …, u_s]

IEEE Access, 2020
In this article, we construct some MDS quantum error-correcting codes (QECCs) from classes of constacyclic codes over Rs = Fp + u1Fp + ··· + usFp, ui2 = ui, uiuj = ujui = 0, for odd prime p and i, j = 1, 2,⋯, s, i ≠ j ...
Hai Q. Dinh, Tushar Bag, Sachin Pathak, Ashish Kumar Upadhyay, Warattaya Chinnakum   +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 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

b-Symbol Distance of Constacylic Codes of Length p^s Over F_p^m + uF_p^m

IEEE Access, 2020
In this research paper, the repeated-root constacyclic codes over the chain ring Fpm + uFpm are considered, where p is a prime and m > 0 is any integer. The b-symbol distance for prime power length, i.e.
H. Q. Dinh, Atul Gaur, A. K. Singh, Manoj Kumar Singh, W. Yamaka   +4 more
doaj   +1 more source

On Symbol-Triple Distance of a Class of Constacyclic Codes of Length 3p^s Over F_p^m + uF_p^m

IEEE Access, 2023
Let $p\not =3$ be any prime. In this paper, we completely determine symbol-triple distance of all $\gamma $ -constacyclic codes of length $3p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , where
Hai Q. Dinh, Bac T. Nguyen, Hiep T. Luu, Woraphon Yamaka   +3 more
doaj   +1 more source

MDS Symbol-Pair Repeated-Root Constacylic Codes of Prime Power Lengths Over $\mathbb F_{p^m}+ u \mathbb F_{p^m}$

IEEE Access, 2019
MDS codes have the highest possible error-detecting and error-correcting capability among codes of given length and size. Let p be any prime, and s, m be positive integers.
H. Q. Dinh, P. Kumam, P. Kumar, S. Satpati, A. K. Singh, W. Yamaka   +5 more
doaj   +1 more source

Some Constacyclic Codes over Finite Chain Rings [PDF]

, 2012
For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that $\lambda$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes.
Batoul, Aicha, Guenda, Kenza, Gulliver, T. Aaron   +2 more
core   +1 more source