Results 1 to 10 of about 55 (53)

Quantum Codes from Galois Hulls of Constacyclic Codes over a Finite Non-Chain Ring [PDF]

Entropy
We study the algebraic structures of constacyclic codes over a new finite non-chain ring R and their l-Galois dual codes based on a new Gray map ϕ and determine the dimensions of the l-Galois hull of constacyclic codes over R.
Enbin Zhang, Bo Kong, Xiying Zheng
doaj   +2 more sources

Hulls of Non-Separable Constacyclic Codes over ${\mathbb{F}}_{\mathit{q}}\mathfrak{R}$ and Their Applications in Constructing New QECCs [PDF]

Entropy
Let R=Fq[u1,u2,u3]/⟨ui2=ui,uiuj=ujui=0⟩ and FqR={(a,d)|a∈Fq,d∈R}, where q=pm, p is a prime, and m∈N+. We investigate the algebraic structure of the non-separable constacyclic codes over the mixed-alphabet ring FqR and then determine the generator ...
Xiying Zheng, Bo Kong, Enbin Zhang
doaj   +2 more sources

Lower Bound on the Minimum Distance of Single-Generator Quasi-Twisted Codes

Mathematics, 2023
We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes.
Adel Alahmadi, Patrick Solé, Ramy Taki Eldin   +2 more
doaj   +1 more source

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

Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established ...
Castillo-Guillén C. A., Álvarez-García C.   +1 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

Some Results on Images of a Class of λ-Constacyclic Codes Over Finite Fields

IEEE Access, 2020
In this paper, we show that any λ-constacyclic code over Fqm is a λ-constacyclic code over Fq under some special maps. Moreover, we show that the images of these λ_constacyclic codes can be put into the concatenated form.
Jian Gao, Juan Li, Yongkang Wang
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