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MDS Constacyclic Codes and MDS Symbol-Pair Constacyclic Codes [PDF]

IEEE Access, 2021
Symbol-pair codes are used to protect against symbol-pair errors in high density data storage systems. One of the most important tasks in symbol-pair coding theory is to design MDS codes.
Hai Q. Dinh, Bac T. Nguyen, Abhay Kumar Singh, Woraphon Yamaka   +3 more
doaj   +3 more sources

Skew Constacyclic Codes over a Non-Chain Ring [PDF]

Entropy, 2023
In this paper, we investigate the algebraic structure of the non-local ring Rq=Fq[v]/⟨v2+1⟩ and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this ring. Furthermore, we give a
Mehmet Emin Köroğlu, Mustafa Sarı
doaj   +6 more sources

On the construction of constacyclically permutable codes from constacyclic codes

AIMS Mathematics
In this paper, we propose a way to partition any constacyclic code over a finite field in its equivalence classes according to the algebraic structure of the code.
Guanghui Zhang , Shuhua Liang
doaj   +3 more sources

$ (\theta_i, \lambda) $-constacyclic codes and DNA codes over $ \mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4} $

AIMS Mathematics
In this paper, three new automorphisms were identified over the ring $ \mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4} $ where $ u^3 = u^2 $. With the help of these automorphisms, the characteristic structures of the generator polynomials for the ...
Fatma Zehra Uzekmek , Elif Segah Oztas, Mehmet Ozen   +2 more
doaj   +3 more sources

Asymmetric Entanglement-Assisted Quantum MDS Codes Constructed from Constacyclic Codes [PDF]

Entropy, 2023
Due to the asymmetry of quantum errors, phase-shift errors are more likely to occur than qubit-flip errors. Consequently, there is a need to develop asymmetric quantum error-correcting (QEC) codes that can safeguard quantum information transmitted ...
Jianzhang Chen, Wanchuan Fang, Shuo Zhou, Jie Qiu, Chenyang Zhang, Yixin Xu, Bozhe Zeng, Youqin Chen   +7 more
doaj   +2 more sources

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

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   +2 more sources

Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
The family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p5 elements (p a prime) and nilpotency index 4 are given.
Castillo-Guillén C. A., Rentería-Márquez C.   +1 more
doaj   +2 more sources

Equivalence of constacyclic codes over finite non-chain ring and quantum codes

AIMS Mathematics
Let $ \mathfrak {R}_{l} = {\mathbb F}_{q}[u]/ \langle u^{l}-u \rangle $, where $ q = p^m $, $ p $ is a prime, and $ m \in \mathbf{N^+} $, $ (l-1)\mid(p-1) $.
Jie Liu, Xiying Zheng
doaj   +2 more sources

A Special Class of Repeated-Root Constacyclic Codes

Asian journal of mathematics and computer research
Let \(\mathbb{F}\)q be a finite field with q elements where q be a prime power. Among the classes of constacyclic codes of length 5ℓps over \(\mathbb{F}\)q we define an equivalence relation such that the classes of constacyclic codes which have the same ...
Ke Wang
openalex   +3 more sources