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研究了环R=F_3+uF_3+vF_3+uvF_3上循环码的结构(u~2=u,v~2=v,uu=uu),证明了该环上的循环码是主理想生成的,并给出了其上循环码的生成多项式. 相似文献
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张晓燕 《数学的实践与认识》2011,41(9)
摘要:引入了环F_2+uF_2+u~2F_2与F_2之间的广义Gray映射,利用环F_2+uF_2+u~2F_2上线性码的生成矩阵得出了广义Gray像φ(C)的生成矩阵,证明了F_2+uF2+u2F2上线性码自正交码的广义Gray像仍为自正交码和F_2+uF_2+u~2F_2上循环码的广义Gray像是F_2上的准循环码. 相似文献
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记环R=F_(p~k)+uF_(p~k)+u~2F_(p~k),定义了一个从R~n到F_(p~k)~(2np~k)的Gray映射.利用Gray映射的性质,研究了环R上(1-u~2)-循环码和循环码.证明了环R上码是(1-u~2)-循环码当且仅当它的Gray象是F_(p~k)上的准循环码.当(n,p)=1时,证明了环R上的长为n的线性循环码的Gray象置换等价于域F_(p~k)上的线性准循环码. 相似文献
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最近,Cassuto和Blaum提出了符号对码的概念,其符号对码的距离(简称符号对距离)与经典纠错码的汉明距离类似,它也是衡量符号对码纠错能力的一个重要参数.而本文作者主要研究了环F_2+uF_2上长度为2~e的循环码的符号对距离,完全确定了每一类循环码的极小符号对距离的精确值. 相似文献
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研究了环F2+uF2上长度为2n(n为奇数)的循环码,给出了循环码及其对偶码的生成多项式,以及循环码为自对偶码的充要条件,最后进一步给出了循环码极小Lee重量的一些相关结论 相似文献
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定义了环R=F2+uF2+u2 F2(u3=0)到F32的一个新的Gray映射.首先介绍环R上奇长度的循环码的挠码,给出了各阶挠码的生成多项式.利用一阶挠码与二阶挠码确立了R上奇长度的循环码的Gray距离. 相似文献
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设q为素数的方幂,F_q为q元有限域.本文通过将F_q上向量的深度概念推广到环R=F_3+vF_3(v~2=1)上,给出R上线性码码字深度的递归算法,进而利用环R上线性码的生成矩阵及环R到F_3的两个加群同态,给出环R上任意长度的线性码深度谱的上下界.并由此推出环R_1=F_P+vF_P(v~2=1)上任意长度的非零线性码深度谱的上下界,其中p为奇质数. 相似文献
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利用环F2+uF2上长为2e的循环码结构,证明了这样的循环码的一类码在Gray映射下的象是循环码,并给出了环F2+uF2上长为2e的循环码的Gray象仍是循环码的一个充要条件. 相似文献
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本文研究了环Fpm+uFpm+u2Fpm上长度为ps的循环码分类.通过建立环Fpm+uFpm+u2Fpm到环Fpm+uFpm的同态,给出了环Fpm+uFpm+u2Fpm上长度为ps的循环码的新分类方法.应用这种方法,得到了环Fpm+uFpm+u2Fpm长度为ps的循环码的码词数. 相似文献
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Alexander Nenashev 《K-Theory》2005,34(3):219-232
We interpret the Steinberg symbols xi,j(a) as homotopies contracting the elementary matrices ei,j(a), the latters being represented by certain arcs in a simplicial model of the K-theory. We further prove the Steinberg relations for these homotopies. This provides an explicit map from K2 of a ring, defined classically as ker(St(R) → GL(R)), to π2 of the G-construction assigned to R. Though the two groups are known to be isomorphic, a certain work is to be done to prove that this explicit map is an isomorphism.
Mathematics Subject Classification 1991: Primary 19B99, 19D99; secondary 18E10, 18F25. 相似文献
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In this paper, we study cyclic codes over the rings Z
2 + uZ
2 and Z
2 + uZ
2 + u
2
Z
2 . We find a set of generators for these codes. The rank, the dual, and the Hamming distance of these codes are studied as
well. Examples of cyclic codes of various lengths are also studied.
相似文献
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Mariya Ishteva Lieven De Lathauwer P.-A. Absil Sabine Van Huffel 《Numerical Algorithms》2009,51(2):179-194
An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric
Newton method for computing the best rank-(R
1, R
2, R
3) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate
the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order
orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324–1342, 2000). This kind of algorithms are useful for many problems.
This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by
the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility
rests with its authors. Research supported by: (1) Research Council K.U.Leuven: GOA-Ambiorics, CoE EF/05/006 Optimization
in Engineering (OPTEC), (2) F.W.O.: (a) project G.0321.06, (b) Research Communities ICCoS, ANMMM and MLDM, (3) the Belgian
Federal Science Policy Office: IUAP P6/04 (DYSCO, “Dynamical systems, control and optimization”, 2007–2011), (4) EU: ERNSI.
M. Ishteva is supported by a K.U.Leuven doctoral scholarship (OE/06/25, OE/07/17, OE/08/007), L. De Lathauwer is supported
by “Impulsfinanciering Campus Kortrijk (2007–2012)(CIF1)” and STRT1/08/023. 相似文献
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A subset MX of a normed linear space X is a Chebyshev set if, for every xX, the set of all nearest points from M to x is a singleton. We obtain a geometrical characterisation of approximatively compact Chebyshev sets in c0. Also, given an approximatively compact Chebyshev set M in c0 and a coordinate affine subspace Hc0 of finite codimension, if M∩H≠, then M∩H is a Chebyshev set in H, where the norm on H is induced from c0. 相似文献
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In this work, we focus on cyclic codes over the ring
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} , which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et.al. in (Des Codes Crypt 42:273–287,
2007) to characterize the ring
(\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2)/(xn-1){({{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2})/(x^n-1)} and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} under two Gray maps that are defined. We also characterize the binary images of cyclic codes over
\mathbbF2+u\mathbbF2+v\mathbbF2+uv\mathbbF2{{{\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2}} in general. 相似文献