Results 71 to 80 of about 1,045 (128)

Construction of New Matrix-Product Codes and Their Applications

IEEE Access, 2019
In this paper, from special code chains $\mathcal {C}_{1} \supseteq \mathcal {C}_{2}~\supseteq \mathcal {C}_{3}$ such that $\mathcal {C}^{\bot _{h}}_{1}\subseteq \mathcal {C}_{3}$ and $\mathcal {C}^{\bot _{h}}_{2}\subseteq \mathcal {C}_{2}$ , some ...
Hao Song, Ruihu Li, Junli Wang, Jingjie Lv   +3 more
doaj   +1 more source

Gray Images of Constacyclic Codes Over Some Polynomial Residue Rings

پژوهش‌های ریاضی, 2021
Let  be the quotient ring    where  is the finite field of size   and  is a positive integer. A Gray map  of length  over  is a special map from  to ( .
Reza Sobhani
doaj  

A note on the duals of skew constacyclic codes

CoRR, 2016
Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $θ: \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of $\mathbb{F}_q^n$ which are invariant under the action of a semi-linear map $Φ_{α,θ}:\mathbb{F}_q^n\to\mathbb{F}_q^n$, defined by $Φ_{α,θ ...
Alexis Eduardo Almendras Valdebenito, Andrea Luigi Tironi   +1 more
openaire   +2 more sources

On ZpZp[u, v]-additive cyclic and constacyclic codes

, 2019
Let $\mathbb{Z}_{p}$ be the ring of residue classes modulo a prime $p$. The $\mathbb{Z}_{p}\mathbb{Z}_{p}[u,v]$-additive cyclic codes of length $(\alpha,\beta)$ is identify as $\mathbb{Z}_{p}[u,v][x]$-submodule of $\mathbb{Z}_{p}[x]/\langle x^{\alpha}-1 ...
Islam, Habibul, Prakash, Om
core  

$m$-adic residue codes over $\mathbb{F}_q[v]/(v^s-v)$

, 2018
Due to their rich algebraic structure, cyclic codes have a great deal of significance amongst linear codes. Duadic codes are the generalization of the quadratic residue codes, a special case of cyclic codes.
Koroglu, Mehmet E., Kuruz, Ferhat, Temiz, Fatih   +2 more
core  

Skew Cyclic and Skew Constacyclic Codes over a Mixed Alphabet

Axioms
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.
Karthick Gowdhaman, Cruz Mohan, Chinnapillai Durairajan, Selda Çalkavur, Patrick Solé   +4 more
doaj   +1 more source

Entanglement-Assisted Quantum Codes from Cyclic Codes. [PDF]

Entropy (Basel), 2022
Pereira FRF, Mancini S.
europepmc   +1 more source

Some New Quantum BCH Codes over Finite Fields. [PDF]

Entropy (Basel), 2021
Xing L, Li Z.
europepmc   +1 more source

Structure and Enumeration of Constacyclic Codes over Cube-Zero Local Rings of Order q⁵

Mathematics
We investigate λ-constacyclic codes of length n over finite commutative local rings R of characteristic p and order q5, where q=pm is an odd prime power, whose Jacobson radical N satisfies N3=0≠N2, under the coprimality condition gcd(n,p)=1.
Sami H. Saif, Shayea Aldossari
doaj   +1 more source

A Note on Factorization and the Number of Irreducible Factors of xⁿ − λ over Finite Fields

Mathematics
Let Fq be a finite field, and let n be a positive integer such that gcd(q,n)=1. The irreducible factors of xn−1 and xn−λ are fundamental concepts with wide applications in cyclic codes and constacyclic codes.
Jinle Liu, Hongfeng Wu
doaj   +1 more source