Results 21 to 30 of about 2,432,274 (184)

New quantum codes from skew constacyclic codes

Advances in Mathematics of Communications, 2021
In the paper under review, the authors construct quantum codes from skew constacyclic codes over the finite commutative non-chain ring of order \(p^{2^{\ell} m}\) with characteristic odd prime \(p\): \[ R_{\ell,m} = \mathbb{F}_{p^m}[v_1,v_2,\dots,v_{\ell}]/\langle v^2_i-1, v_iv_j-v_jv_i\rangle_{1\leq i, j\leq \ell}, \] where \(m\) and \(\ell\) are ...
Ram Krishna Verma, Om Prakash, Ashutosh Singh, Habibul Islam   +3 more
openalex   +4 more sources

CONSTACYCLIC CODES OVER LIPSCHITZ INTEGERS

Matematički Vesnik, 2023
Summary: In this paper, the goal is to obtain constacyclic codes over Lipschitz integers in terms of Lipschitz metric. A decoding procedure is proposed for these codes, some of which have been shown to be perfect codes. Performance of constacyclic codes over Lipschitz integers is investigated over Additive White Gaussian Channel (AWGN) by means of ...
Guzeltepe, Murat, Cetinel, Gokcen, Sazak, Nukhet   +2 more
openaire   +2 more sources

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

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

Quantum codes from $ \sigma $-dual-containing constacyclic codes over $ \mathfrak{R}_{l, k} $

AIMS Mathematics, 2023
Let $ \mathfrak{R}_{l, k} = {\mathbb F}_{p^m}[u_1, u_2, \cdots, u_k]/ \langle u_{i}^{l} = u_{i}, u_iu_j = u_ju_i = 0 \rangle $, where $ p $ is a prime, $ l $ is a positive integer, $ (l-1)\mid(p-1) $ and $ 1\leq i, j\leq k $. First, we define a Gray map $
Xiying Zheng, Bo Kong, Yao Yu
doaj   +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

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

Repeated-Root Constacyclic Codes Over the Chain Ring F_p^m[u]/⟨u³⟩

IEEE Access, 2020
Let Z = Fpm[u]/(u3) be the finite commutative chain ring, where p is a prime, m is a positive integer and Fpm is the finite field with pm elements. In this paper, we determine all repeated-root constacyclic codes of arbitrary lengths over Z and their ...
Tania Sidana, Anuradha Sharma
doaj   +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