MDS constacyclic codes and MDS symbol-pair constacyclic codes

HQ Dinh, BT Nguyen, AK Singh, W Yamaka - IEEE Access, 2021 - ieeexplore.ieee.org
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 …

Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length

HQ Dinh, BT Nguyen, M Paravee, HL Thi… - Quantum Information …, 2023 - Springer
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 3 ps over F pm. We obtain …

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

HQ Dinh, HT Le, BT Nguyen, P Maneejuk - IEEE Access, 2021 - ieeexplore.ieee.org
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 over. We obtain several …

On a class of skew constacyclic codes over mixed alphabets and applications in constructing optimal and quantum codes

HQ Dinh, T Bag, K Abdukhalikov, S Pathak… - Cryptography and …, 2023 - Springer
In this paper, we first discuss linear codes over R and present the decomposition structure of
linear codes over the mixed alphabet F q R, where R= F q+ u F q+ v F q+ uv F q, with u 2= 1 …

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

HQ Dinh, T Bag, S Pathak, AK Upadhyay… - IEEE …, 2020 - ieeexplore.ieee.org
In this article, we construct some MDS quantum error-correcting codes (QECCs) from
classes of constacyclic codes over R s= F p+ u 1 F p+···+ us F p, ui 2= ui, uiuj= ujui= 0, for …

Constacyclic Codes of Length 3ps Over Fpm + uFpm and Their Application in Various Distance Distributions

HQ Dinh, BT Nguyen, W Yamaka - IEEE Access, 2020 - ieeexplore.ieee.org
Let p≠ 3 be any prime. The structures of all λ-constacyclic codes of length 3p s over the
finite commutative chain ring Fp m+ uFp m (u 2= 0) are established in the term of their …

On F2RS-cyclic codes and their applications in constructing optimal codes

HQ Dinh, S Pathak, T Bag, AK Upadhyay, R Bandi… - Discrete …, 2021 - Elsevier
Abstract Let R= F 2+ u F 2 (u 2= 0) and S= F 2+ u F 2+ u 2 F 2 (u 3= 0) be two finite
commutative chain rings. This paper studies F 2 R S-cyclic codes, which are described as S …

MDS constacyclic codes of prime power lengths over finite fields and construction of quantum MDS codes

HQ Dinh, RT ElDin, BT Nguyen… - International Journal of …, 2020 - Springer
If we fix the code length n and dimension k, maximum distance separable (briefly, MDS)
codes form an important class of codes because the class of MDS codes has the greatest …

[PDF][PDF] Constacyclic codes of length 8 ps over F p m+ u F pm

HQ Dinh, BT Nguyen, M Paravee - Adv. Math. Commun. https://doi …, 2022 - academia.edu
For any odd prime p, the structures and duals of λ-constacyclic codes of length 8ps over R=
Fpm+ uFpm are completely determined for all unit λ of the form λ= ξl∈ Fpm, where l is even …

An explicit expression for Euclidean self-dual cyclic codes of length 2k over Galois ring GR (4, m)

Y Cao, Y Cao, S Ling, G Wang - Finite Fields and Their Applications, 2021 - Elsevier
For any positive integers m and k, existing literature only determines the number of all
Euclidean self-dual cyclic codes of length 2 k over the Galois ring GR (4, m), such as in Kiah …