共查询到20条相似文献,搜索用时 15 毫秒
1.
Zi-hui Liu 《应用数学学报(英文版)》2011,27(1):141-148
The properties of the generator matrix are given for linear codes over finite commutative chain rings,and the so-called almost-MDS (AMDS) codes are studied. 相似文献
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研究了有限链环R上常循环码的等价性,根据等价性给出了R上一些常循环码及其对偶码的结构.确定了该环上长度为ps的所有常循环码及其对偶码的结构. 相似文献
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In this article, we study negacyclic self-dual codes of length n over a finite chain ring R when the characteristic p of the residue field [`(R)]{\bar{R}} and the length n are relatively prime. We give necessary and sufficient conditions for the existence of (nontrivial) negacyclic self-dual
codes over a finite chain ring. As an application, we construct negacyclic MDR self-dual codes over GR(p
t
, m) of length p
m
+ 1. 相似文献
8.
《Discrete Mathematics》2022,345(4):112767
Let R be a finite commutative chain ring, be the dihedral group of size 2n and be the dihedral group ring. In this paper, we completely characterize left ideals of (called left -codes) when . In this way, we explore the structure of some skew-cyclic codes of length 2 over R and also over , where S is an isomorphic copy of R. As a particular result, we give the structure of cyclic codes of length 2 over R. In the case where is a Galois field, we give a classification for left -codes over , for any positive integer N. In both cases we determine dual codes and identify self-dual ones. 相似文献
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In this paper, is a finite chain ring with residue field and is a unit in By assuming that the multiplicative order of is coprime to we give the trace-representation of any simple-root -constacyclic code over of length and on the other hand show that any cyclic code over of length is a direct sum of trace-representable cyclic codes. Finally, we characterize the simple-root, contractable and cyclic codes over of length into -constacyclic codes of length 相似文献
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LetR be a finite commutative ring with identity and τ be a nonnegative integer. In studying linear finite automata, one of the
basic problems is how to characterize the class of rings which have the property that every (weakly) invertible linear finite
automaton ℳ with delay τ over R has a linear finite automaton ℳ′ over R which is a (weak) inverse with delay τ of ℳ. The rings
and linear finite automata are studied by means of modules and it is proved that *-rings are equivalent to self-injective
rings, and the unsolved problem (for τ=0) is solved. Moreover, a further problem of how to characterize the class of rings
which have the property that every invertible with delay τ linear finite automaton ℳ overR has a linear finite automaton ℳ′ over R which is an inverse with delay τ′ for some τ′⩾τ is studied and solved.
Project supported by the National Natural Science Foundation of China(Grant No. 69773015). 相似文献
13.
Additive cyclic codes over Galois rings were investigated in Cao et al. (2015). In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in Cao et al. (2015), whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples. 相似文献
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In this paper, we give necessary and sufficient conditions for the existence of non-trivial cyclic self-dual codes over finite chain rings. We prove that there are no free cyclic self-dual codes over finite chain rings with odd characteristic. It is also proven that a self-dual code over a finite chain ring cannot be the lift of a binary cyclic self-dual code. The number of cyclic self-dual codes over chain rings is also investigated as an extension of the number of cyclic self-dual codes over finite fields given recently by Jia et al. 相似文献
15.
Eimear Byrne Marcus Greferath Michael E. O’Sullivan 《Designs, Codes and Cryptography》2007,42(3):289-301
In traditional algebraic coding theory the linear-programming bound is one of the most powerful and restrictive bounds for
the existence of both linear and non-linear codes. This article develops a linear-programming bound for block codes on finite
Frobenius rings.
An erratum to this article can be found at 相似文献
16.
Summary. We propose an algorithm for the numerical solution of
large-scale symmetric positive-definite linear complementarity problems.
Each step of the algorithm combines an application of the successive
overrelaxation
method with projection (to determine an approximation of the optimal active
set) with the preconditioned conjugate gradient method (to solve the reduced
residual systems of linear equations). Convergence of the iterates to the
solution is proved. In the experimental part we compare the efficiency of the
algorithm with several other methods. As test example we consider the
obstacle problem with different obstacles.
For problems of dimension up to 24\,000 variables, the algorithm finds the
solution in less then 7 iterations, where each iteration
requires about 10
matrix-vector multiplications.
Received July 14, 1993 / Revised version received February 1994 相似文献
17.
《Applied mathematics and computation》1986,18(4):313-353
A general procedure is given for solving large sets of linear equations by first rewriting them in a form suitable for aggregation of both the variables and equations, followed by disaggregation. A computational algorithm which iteratively aggregates and disaggregates is shown to converge geometrically to the exact solution. Provided the original problem has a structure suitable for such aggregation, the algorithm exhibits fast computation times, small main-memory requirements, and robustness to the starting point. A rigorous foundation for aggregation and disaggregation is provided by the equations employed by this algorithm. 相似文献
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In light of the generator polynomials of constacyclic codes over finite chain rings, the depth spectrum of constacyclic codes can be determined if (n,p)=1. 相似文献
19.
Morou Amidou 《Linear algebra and its applications》2008,429(7):1687-1698
We present a new and simple algorithm for completion of unimodular vectors with entries in a multivariate Laurent polynomial ring over an infinite field K. More precisely, given n?3 and a unimodular vector V=t(v1,…,vn)∈Rn (that is, such that 〈v1,…,vn〉=R), the algorithm computes a matrix M in Mn(R) whose determinant is a monomial such that MV=t(1,0,…,0), and thus M-1 is a completion of V to an invertible matrix. 相似文献