Zobrazeno 1 - 10
of 909
pro vyhledávání: '"Gray map"'
Autor:
Yildirim Tulay
Publikováno v:
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 32, Iss 3, Pp 173-192 (2024)
In this study, we focus on skew cyclic codes over the family of rings 𝔽q S where q is a power of a prime number and S = 𝔽q + v𝔽q with v2 = v. Structural properties of these codes are studied in detail. Obtained results lead us to characteriz
Externí odkaz:
https://doaj.org/article/d223de94723046c1a625d15743a2de7a
Publikováno v:
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 32, Iss 1, Pp 19-44 (2024)
Let S = ℤp[u, v]/〈u2, v2, uv − uv〉 be a semi-local ring, where p is a prime number. In the present article, we determine the generating sets of S and use them to construct the structures of ℤpS-additive cyclic and constacyclic codes. The mi
Externí odkaz:
https://doaj.org/article/7bc70dbd6cb94a54a59089f4b7b0ca83
Publikováno v:
AIMS Mathematics, Vol 9, Iss 3, Pp 7396-7413 (2024)
Let $ s \geq 1 $ be a fixed integer. In this paper, we focus on generating cyclic codes over the ring $ \mathcal{R}(\alpha_1, \alpha_2, \ldots, \alpha_s) $, where $ \alpha_i \in \mathbb{F}_q\backslash \{0\} $, $ 1 \leq i \leq s $, by using the Gray m
Externí odkaz:
https://doaj.org/article/745031ec1ded4a2f8fd7dac1bfc93d7f
Autor:
Mohd Arif Raza, Mohammad Fareed Ahmad, Adel Alahmadi, Widyan Basaffar, Manish K. Gupta, Nadeem ur Rehman, Abdul Nadim Khan, Hatoon Shoaib, Patrick Sole
Publikováno v:
Axioms, Vol 13, Iss 10, p 697 (2024)
The main focus of this paper is to analyze the algebraic structure of constacyclic codes over the ring R=Fp+w1Fp+w2Fp+w22Fp+w1w2Fp+w1w22Fp, where w12−α2=0, w1w2=w2w1, w23−β2w2=0, and α,β∈Fp∖{0}, for a prime p. We begin by introducing a Gr
Externí odkaz:
https://doaj.org/article/bbc2e9b7c3e3410a82112c3685547684
Publikováno v:
Mathematics, Vol 12, Iss 13, p 2014 (2024)
In this paper, we investigate cyclic codes over the ring E of order 4 and characteristic 2 defined by generators and relations as E=⟨a,b∣2a=2b=0,a2=a,b2=b,ab=a,ba=b⟩. This is the first time that cyclic codes over the ring E are studied. Each cy
Externí odkaz:
https://doaj.org/article/3bb8905c487d417da7496061f3d0e391
Autor:
Xuesong Si, Chuanze Niu
Publikováno v:
AIMS Mathematics, Vol 8, Iss 10, Pp 24434-24445 (2023)
The algebraic structure of skew cyclic codes over $ M_{2} $($ \mathbb{F}_2 $), using the $ \mathbb{F}_4 $-cyclic algebra, is studied in this work. We determine that a skew cyclic code with a polynomial of minimum degree $ d(x) $ is a free code genera
Externí odkaz:
https://doaj.org/article/99c7d6899ddb4c478be5aec8afaa9b84
Publikováno v:
Axioms, Vol 13, Iss 6, p 360 (2024)
In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet R=FqR1R2, where q=pm, p is an odd prime with m odd and R1=Fq+uFq with u2=u, and R2=Fq+uFq+vFq with u2=u,v2=v,uv=vu=0. Such codes consist of the juxtaposition of th
Externí odkaz:
https://doaj.org/article/4d394ace72ae447ebef99a59faa821f7
Publikováno v:
IEEE Access, Vol 11, Pp 92898-92912 (2023)
In this paper, we investigate self-dual double circulant, and self-dual and linear complementary dual (LCD) double negacirculant codes over a finite ring $R = \mathbb F_{q} + u \mathbb F_{q} + v \mathbb F_{q} + uv\mathbb F_{q}$ , where $u^{2}=u$ , $v
Externí odkaz:
https://doaj.org/article/4c927dc87fab4826ada2368653a939cb
Publikováno v:
Discussiones Mathematicae - General Algebra and Applications, Vol 42, Iss 2, Pp 349-362 (2022)
In this paper, we study the structure of cyclic codes overM2(ℤ4) (the matrix ring of matrices of order 2 over ℤ4), which is perhaps the first time that the ring is considered as a code alphabet. This ring is isomorphic to ℤ4[w] + Uℤ4[w], wher
Externí odkaz:
https://doaj.org/article/d2f67433423d49b0a83aca9cfbbb44d4
Autor:
Kong Bo, Zheng Xiying
Publikováno v:
Open Mathematics, Vol 20, Iss 1, Pp 1013-1020 (2022)
Let q=pmq={p}^{m}, pp be an odd prime, and Rk=Fq[u1,u2,…,uk]/⟨ui3=ui,uiuj=ujui⟩{R}_{k}={{\mathbb{F}}}_{q}\left[{u}_{1},{u}_{2},\ldots ,{u}_{k}]\hspace{-0.08em}\text{/}\hspace{-0.08em}\langle {u}_{i}^{3}={u}_{i},{u}_{i}{u}_{j}={u}_{j}{u}_{i}\ran
Externí odkaz:
https://doaj.org/article/4491cc9fc79c490e9c1a3504f8fbce77