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为了研究“确定κ维q元线性码几乎所有重量谱”这个难题,我们需要用Klφve的一组必要条件来引入重量谱的分类.易知类数f(κ)=2(κ-2)(κ-3)/2.本文得到了这些必要条件之间的关系,使得f(κ)减少了很多.本文还用递推方法与含0,1元素的表格给出了描述每一类的必要条件. 相似文献
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王开弘 《数学的实践与认识》2008,38(12):141-144
通过对q元线性码广义Hamming重量dr(·)的分析,应用支撑重量ωs(C)的性质,再次分析了q元[n,k]线性码广义Griesmer界n≥dr+sum from i=1 to k-r[(q-1)dr/qi(qr-1)]. 相似文献
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通过定义δ(xi,yi)函数,把2元非线性2-重量码(n,2,ω1,ω2)的性质推广到q元非线性2-重量码(n,2,ω1,ω2)上,根据码的距离分布和对偶距离分布讨论了码C的不可检错概率.给出了码C不是最佳检错码的几个条件. 相似文献
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当信息在第二类窃密信道中传输时,线性码的广义汉明重量谱完全描述的它在该信道中的密码学特征.计算一个线性码的广义汉明重量谱是一个基本问题,首先提出了线性码的“最简基”的概念.在此基础上给出了一般线性码子码的几种计数公式,并给出了它们之间等价性的证明. 相似文献
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本文研究了环R=F4+v F4上线性码及重量分布.利用环R=F4+v F4到F2的一种Gray映射?,证明了环上R线性码C的Gray像?(C)的对偶码为?(C⊥).然后,利用域F2上线性码与对偶码的重量分布的关系及Gray映射性质,给出了该环上线性码与对偶码之间的各种重量分布的Macwilliams恒等式. 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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Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of a linear code has many applications such as on the type II wire-tap channel, dealing with t-resilient functions and trellis or branch complexity of linear codes and so on. In this paper, we present a formula for computing the weight hierarchies of linear codes constructed by the generalized method of defining sets. Then, we construct two classes of binary linear codes with a few weights and determine their weight distributions and weight hierarchies completely. Some codes of them can be used in secret sharing schemes. 相似文献
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Finite Projective Geometries and Classification of the Weight Hierarchies of Codes (Ⅰ) 总被引:1,自引:0,他引:1
WenDeCHEN TorleivKLφVE 《数学学报(英文版)》2004,20(2):333-348
The weight hierarchy of a binary linear [n,κ] code C is the sequence (d1,d2,...,dκ), where dr is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries.The possible weight hierarchies in class A, B, C, D are determined in Part (Ⅰ). The possible weight hierarchies in class E, F, G, H, I are determined in Part (Ⅱ). 相似文献
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In this paper, by using a new kind of geometric structures, we present some sufficient conditions to determine the weight hierarchies of linear codes satisfying the chain condition. 相似文献
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《Discrete Mathematics》2022,345(3):112718
Weight hierarchies of linear codes have been an interesting topic due to their important values in theory and applications in cryptography. In this paper, we restrict a degenerate quadratic form f over a finite field of odd characteristic to subspaces and introduce a quotient space related to the degenerate quadratic form f. From the polynomial f over the quotient space, a non-degenerate quadratic form is induced. Some related results on the subspaces and quotient spaces are obtained. Based on these results, the weight hierarchies of a family of linear codes related to f are determined. 相似文献
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It is well known that he influence relation orders the voters the same way as the classical Banzhaf and Shapley–Shubik indices do when they are extended to the voting games with abstention (VGA) in the class of complete games. Moreover, all hierarchies for the influence relation are achievable in the class of complete VGA. The aim of this paper is twofold. Firstly, we show that all hierarchies are achievable in a subclass of weighted VGA, the class of weighted games for which a single weight is assigned to voters. Secondly, we conduct a partial study of achievable hierarchies within the subclass of H-complete games, that is, complete games under stronger versions of influence relation. 相似文献
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V. L. Selivanov 《Algebra and Logic》2002,41(5):337-348
A new, logical approach is propounded to resolve the decidability problem for the hierarchies of Straubing and Brzozowski based on preservation theorems in model theory, a theorem of Higman, and the Rabin tree theorem. We thus manage to obtain purely logical, short proofs of some known decidability facts, which definitely may be of methodological interest. The given approach also applies in some other similar situations, for instance, to the hierarchies of formulas modulo a theory of linear orderings with finitely many unary predicates. 相似文献
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Enrique G. Reyes 《Journal of Differential Equations》2006,225(1):26-56
Hierarchies of evolution equations of pseudo-spherical type are introduced, thereby generalizing the notion of a single equation describing pseudo-spherical surfaces due to S.S. Chern and K. Tenenblat, and providing a connection between differential geometry and the study of hierarchies of equations which are the integrability condition of sl(2,R)-valued linear problems. As an application, it is shown that there exist local correspondences between any two (suitably generic) solutions of arbitrary hierarchies of equations of pseudo-spherical type. 相似文献
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In our article [ 1 ], "A tree of linearisable second-order evolution equations by generalised hodograph transformations " we present a class of linearizable ( C -integrable) second-order evolution equations in (1+1) dimensions, using a generalized hodograph transformation. We report here the complete set of recursion operators for this class and present the resulting linearizable ( C -integrable) hierarchies in (1+1) dimensions. The autonomous class of linearizable hierarchies are extended further by considering the equations in potential form followed by the pure hodograph transformation. 相似文献
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Enrique G. Reyes 《Results in Mathematics》2011,60(1-4):53-101
This paper surveys some recent developments around the notion of a scalar partial differential equation describing pseudo-spherical surfaces due to Chern and Tenenblat. It is shown how conservation laws, pseudo-potentials, and linear problems arise naturally from geometric considerations, and it is also explained how Darboux and B?cklund transformations can be constructed starting from geometric data. Classification results for equations in this class are stated, and hierarchies of equations of pseudo-spherical type are introduced, providing a connection between differential geometry and the study of hierarchies of equations which are the integrability condition of sl(2, R)-valued linear problems. Furthermore, the existence of correspondences between any two solutions to equations of pseudo-spherical type is reviewed, and a correspondence theorem for hierarchies is also mentioned. As applications, an elementary immersion result for pseudo-spherical metrics arising from the Chern?CTenenblat construction is proven, and non-local symmetries of the Kaup?CKupershmidt, Sawada?CKotera, fifth order Korteweg?Cde Vries and Camassa?CHolm (CH) equation with non-zero critical wave speed are considered. It is shown that the existence of a non-local symmetry of a particular type is enough to single the first three equations out from a whole family of equations describing pseudo-spherical surfaces while, in the CH case, it is shown that it admits an infinite-dimensional Lie algebra of non-local symmetries which includes the Virasoro algebra. 相似文献