Results 31 to 40 of about 1,030 (123)

Constacyclic Codes over Finite Chain Rings of Characteristic p

Axioms, 2021
Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R.
Sami Alabiad, Yousef Alkhamees
doaj   +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

New quantum codes from skew constacyclic codes

Advances in Mathematics of Communications, 2023
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 ...
Verma, Ram Krishna, Prakash, Om, Singh, Ashutosh, Islam, Habibul   +3 more
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Non-binary quantum codes from constacyclic codes over 𝔽q[u1, u2,…,uk]/⟨ui3 = ui, uiuj = ujui⟩

Open Mathematics, 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}\rangle ...
Kong Bo, Zheng Xiying
doaj   +1 more source

On the codes over the Z_3+vZ_3+v^2Z_3

, 2015
In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R=Z_3+vZ_3+v^2Z_3, v^3=v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skew constacyclic codes over
Cengellenmis, Yasein, Dertli, Abdullah, Eren, Senol   +2 more
core   +1 more source

Symbol-Triple Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over ${\mathbb{F}}_q+u{\mathbb{F}}_q+u^2{\mathbb{F}}_q$

Mathematics, 2022
Let p be an odd prime, where ϑ and m are positive integers. Let ψ be a nonzero element of the finite field Fq, where q=pm, and R=Fq+uFq+u2Fq(u3=0). In this paper, we determine completely the symbol-triple distances of all ψ-constacyclic codes of length ...
Hai Q. Dinh, Jamal Laaouine, Brahim Boudine, Woraphon Yamaka   +3 more
doaj   +1 more source

Constacyclic codes as invariant subspaces

Linear Algebra and its Applications, 2009
A constacyclic code (sometimes also referred to as pseudo-cyclic code) is a linear code over a field GF\((q)\) invariant under the permutation \(\psi_a:\) \((c_0,c_1\ldots,c_{n-1})\mapsto (ac_{n-1},c_0,c_1\ldots,c_{n-1})\) (for a fixed field element \(a\)). (In the introduction of the article the definition is not correct).
Radkova, D., van Zanten, A.J.
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Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\)

Mathematics, 2021
Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring.
Mohammed E. Charkani, Hai Q. Dinh, Jamal Laaouine, Woraphon Yamaka   +3 more
doaj   +1 more source

On Skew-Constacyclic Codes

Finite Fields and Their Applications, 2016
Cyclic codes are a well-known class of linear block codes with efficient decoding algorithms. In recent years they have been generalized to skew-constacyclic codes; such a generalization has previously been shown to be useful. We begin with a study of skew-polynomial rings so that we may examine these codes algebraically as quotient modules of non ...
Fogarty, Neville, Gluesing-Luerssen, Heide   +1 more
openaire   +3 more sources