Results 1 to 10 of about 143,950 (277)

MDS and self-dual codes over rings

Finite Fields and Their Applications, 2012
In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ...
Guenda, Kenza, Gulliver, T. Aaron
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On Linear Codes over Local Rings of Order p⁴

Mathematics
Suppose R is a local ring with invariants p,n,r,m,k and mr=4, that is R of order p4. Then, R=R0+uR0+vR0+wR0 has maximal ideal J=uR0+vR0+wR0 of order p(m−1)r and a residue field F of order pr, where R0=GR(pn,r) is the coefficient subring of R.
Sami Alabiad, Alhanouf Ali Alhomaidhi, Nawal A. Alsarori   +2 more
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and [PDF]

The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(pe, l) (including Zpe).
Hamid Kulosman, Steven T. Dougherty
core  

Cyclic codes over finite rings

Discrete Mathematics, 1997
A linear left code \(C\) of length \(n\) over a finite ring \(R\) is a submodule of \({}_R R^n\). It is called splitting if it is a direct summand of \({}_R R^n\). \(C\) is a cyclic linear left code if it is a left ideal of \(R[x]/(x^n -1)\) and it is called splitting if it is a direct summand of \({}_R (R[x]/(x^n -1))\).
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Codes as Modules over Skew Polynomial Rings [PDF]

, 2009
In previous works we considered codes defined as ideals of quotients of skew polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes defined as modules over skew polynomial rings, removing therefore some of the constraints on the length of the skew codes defined as ideals.
Boucher, Delphine, Ulmer, Félix
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$m$-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  

The Depth Distribution of Constacyclic Codes Over $F_p+vF_p$

IEEE Access, 2018
The depth distribution of a linear code was put forward by Etzion as a new characterization for linear codes. The previously known results pay close attention to the depth distribution of the linear codes over chain rings.
Guanghui Zhang
doaj   +1 more source

The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems [PDF]

Quantum
Qudits with local dimension $d \gt 2$ can have unique structure and uses that qubits ($d=2$) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators.
Rahul Sarkar, Theodore J. Yoder
doaj   +1 more source

Algebraic geometric codes over rings

Journal of Pure and Applied Algebra, 1999
Let \(A\) denote a local Artinian ring with finite residue field. Let \(X\) be a smooth curve of genus \(g\) over \(\text{Spec }A\). Given a line bundle \({\mathcal L}\) on \(X\), a set \(\mathcal Z=\{Z_1,\dots,Z_n\}\) of disjoint \(A\)-points on \(X\), and chosen isomorphisms \(\gamma_i: \Gamma(Z_i,{\mathcal L}|_{Z_i})\rightarrow A\), the author ...
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Optimal STBCs from codes over galois rings

2005 IEEE International Conference on Personal Wireless Communications, 2005. ICPWC 2005., 2005
A space-time block code (STBC) C/sub ST/ is a finite collection of n/sub t/ /spl times/ l complex matrices. If S is a complex signal set, then C/sub ST/ is said to be completely over S if all the entries of each of the codeword matrices are restricted to S.
Kiran, T, Rajan, Sundar B
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