Results 21 to 30 of about 158,948 (278)

Skew constacyclic codes over finite chain rings

Advances in Mathematics of Communications, 2012
Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of $x^n- $, where $ $ is a unit element, are exhibited.
Jitman, Somphong, Ling, San, Udomkavanich, Patanee   +2 more
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Contraction of cyclic codes over finite chain rings [PDF]

Discrete Mathematics, 2018
Let $\texttt{R}$ be a commutative finite chain ring of invariants $(q,s)$ and $ (\texttt{R})$ the Teichm ller's set of $\texttt{R}.$ In this paper, the trace representation cyclic $\texttt{R}$-linear codes of length $\ell,$ is presented, when $\texttt{gcd}(\ell, q) = 1.$ We will show that the contractions of some cyclic $\texttt{R}$-linear codes of ...
Fotue Tabue, Alexandre, Mouaha, Christophe   +1 more
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Expanders on matrices over a finite chain ring, I

International Journal of Mathematics, 2023
In this work and its sequel, we study the expanding phenomenon of matrices over a finite chain ring of large residue field. A sum-product estimate is proved. It is shown that [Formula: see text] is a moderate expander on [Formula: see text] matrices with exponent [Formula: see text].
Dung M. Ha, Hieu T. Ngo
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LIFTED CODES OVER FINITE CHAIN RINGS [PDF]

, 2011
In this paper, we study lifted codes over finite chain rings.
Dougherty, Steven T., Liu, Hongwei, Park, Young Ho   +2 more
core   +1 more source

Some conditions for finiteness of a ring

International Journal of Mathematics and Mathematical Sciences, 1988
Extending a result of Putcha and Yaqub, we prove that a non-nil ring must be finite if it has both ascending chain condition and descending chain condition on non-nil subrings.
Howard E. Bell
doaj   +1 more source

Explicit Representation and Enumeration of Repeated-Root (δ + αu²)-Constacyclic Codes Over F₂^m[u]/‹u^2λ›

IEEE Access, 2020
Let F2(m) be a finite field of 2m elements, λ and k be integers satisfying λ, k ≥ 2 and denote R = F2(m)[u]/(u2λ). Let δ, α ∈ F2(m)×.
Yuan Cao, Yonglin Cao, Hai Q. Dinh, Tushar Bag, Woraphon Yamaka   +4 more
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Hamming Distance of Constacyclic Codes of Length p^s Over F_p^m+uF_p^m+u²F_p^m

IEEE Access, 2021
Let $p$ be any prime, $s$ and $m$ be positive integers. In this paper, we completely determine the Hamming distance of all constacyclic codes of length $p^s$ over the finite commutative chain ring $\mathbb {F}_{p^m}+ u\mathbb {F}_{p^m} + u^{2 ...
Hai Q. Dinh, Jamal Laaouine, Mohammed E. Charkani, Warattaya Chinnakum   +3 more
doaj   +1 more source

Chain Polytopes and Algebras with Straightening Laws [PDF]

, 2015
It will be shown that the toric ring of the chain polytope of a finite partially ordered set is an algebra with straightening laws on a finite distributive lattice.
Hibi, Takayuki, Li, Nan
core   +1 more source

On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5p^s Over F_p ^m + uF_p ^m

IEEE Access, 2022
Let $p\not =5$ be any odd prime. Using the algebraic structures of all cyclic codes of length $5p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , in this paper, the exact values of Hamming ...
Hai Q. Dinh, Bac T. Nguyen, Hiep L. Thi, Woraphon Yamaka   +3 more
doaj   +1 more source

LCD codes over finite chain rings

Finite Fields and Their Applications, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xiusheng, Liu, Hualu
openaire   +1 more source