Results 11 to 20 of about 1,030 (123)

Quantum Codes Obtained from Skew ϱ‐λ‐Constacyclic Codes over Rk

Quantum Engineering, Volume 2023, Issue 1, 2023., 2023
Let Rk=Fqu1,u2,⋯,uk/, where q = pm, p is an odd prime, αi is a unit over Fq, and i, j = 1,2, ⋯, k. In this article, we define a Gray map from Rkn to Fqk+1n, we study the structure of skew ϱ‐λ‐constacyclic codes over Rk, and then we give the necessary and sufficient conditions for skew ϱ‐λ‐constacyclic codes over Rk to satisfy dual
Bo Kong, Xiying Zheng, Jie Liu, Hongjing Jiang, Liuguo Yin   +4 more
wiley   +1 more source

Characterizations and Properties of Monic Principal Skew Codes over Rings

Security and Communication Networks, Volume 2022, Issue 1, 2022., 2022
Let A be a ring with identity, σ a ring endomorphism of A that maps the identity to itself, δ a σ‐derivation of A, and consider the skew‐polynomial ring A[X; σ, δ]. When A is a finite field, a Galois ring, or a general ring, some fairly recent literature used A[X; σ, δ] to construct new interesting codes (e.g., skew‐cyclic and skew‐constacyclic codes ...
Mhammed Boulagouaz, Abdulaziz Deajim, Lu Ou   +2 more
wiley   +1 more source

Matrix‐Product Codes over Commutative Rings and Constructions Arising from (σ, δ)‐Codes

Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021
A well‐known lower bound (over finite fields and some special finite commutative rings) on the Hamming distance of a matrix‐product code (MPC) is shown to remain valid over any commutative ring R. A sufficient condition is given, as well, for such a bound to be sharp. It is also shown that an MPC is free when its input codes are all free, in which case
Mhammed Boulagouaz, Abdulaziz Deajim, Marco Fontana   +2 more
wiley   +1 more source

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

Galois self-dual constacyclic codes [PDF]

Designs, Codes and Cryptography, 2016
Key words: Constacyclic code, Galois inner product, $q$-coset function, isometry, Galois self-dual ...
Fan, Yun, Zhang, Liang
openaire   +2 more sources

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

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

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

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