共查询到20条相似文献,搜索用时 15 毫秒
1.
The performance of a linear t-error correcting code over a q-ary symmetric memoryless channel with symbol error probability ε is characterized by the probability that a transmission error will remain undetected. This probability is a function of ε involving the code weight distribution and the weight distribution of the cosets of minimum weight at most t. When the undetectable error probability is an increasing function of ε, the code is called t-proper.
The paper presents sufficient conditions for t-properness and a list of codes known to be proper, many of which have been studied by these sufficient conditions. Special attention is paid to error detecting codes of interest in modern communication. 相似文献
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It is well known that a de Bruijn sequence over has the minimal polynomial (x+1)d, where 2n-1+nd2n-1. We study the minimal polynomials of the modified de Bruijn sequences. 相似文献
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Sndor Gyri 《Discrete Applied Mathematics》2008,156(9):1407-1430
The signature coding for M active users out of T total users over a multiple access OR channel is considered. The mathematical problem is equivalent to the M-cover-free problem of extremal set theory. We survey the upper and lower bounds on the minimal code word length n(T,M), and present some code constructions. According to the current state of the theory, for 1MTso there is a huge gap between the upper and lower bounds. Moreover, there is no known construction approaching the upper bound. 相似文献
4.
Rudolf Ahlswede Ferdinando Cicalese Christian Deppe 《Discrete Applied Mathematics》2008,156(9):1444-1460
The Rényi–Berlekamp–Ulam game is a classical model for the problem of determining the minimum number of queries to find an unknown member in a finite set when up to a finite number of the answers may be erroneous. In the variant considered in this paper, questions with q many possible answers are allowed, further lies are constrained by a bipartite graph with edges weighted by 0,1,2,… (the “channel”). The channel Γ is an arbitrary assignment stipulating the cost of the different possible lies, i.e., of each answer j≠i when the correct answer is i by Γ(i,j). It is also assumed that a maximum cost e (sum of the cost of all wrong answers) can be afforded by the responder during the whole game. We provide tight asymptotic bounds for the number of questions needed to solve this problem. The appropriate searching strategies are actually provided. We also show that adaptiveness can be dramatically reduced when the channel satisfies certain symmetry constraints. 相似文献
5.
Serafino Cicerone Gabriele Di Stefano Dagmar Handke 《Discrete Applied Mathematics》2005,150(1-3):99-120
We introduce the (k,ℓ)-self-spanners graphs to model non-reliable interconnection networks. Such networks can be informally characterized as follows: if at most ℓ edges have failed, as long as two vertices remain connected, the distance between these vertices in the faulty graph is at most k times the distance in the non-faulty graph. By fixing the values k and ℓ (called stretch factor and fault-tolerance, respectively), we obtain specific new graph classes. We first provide characterizational, structural, and computational results for these classes. Then, we study relationships between the introduced classes and special graphs classes (distance-hereditary graphs, cographs, and chordal graphs), and common network topologies (grids, tori, hypercubes, butterflies, and cube-connected cycles) as well. 相似文献
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A. Ballester-Bolinches L.A. Kurdachenko Tatiana Pedraza 《Journal of Pure and Applied Algebra》2007,210(3):665-671
A group G is said to be a -group if permutability is a transitive relation in the set of all subgroups of G. Our purpose in this paper is to study -groups in the class of periodic radical groups satisfying min-p for all primes p. 相似文献
8.
Two uniform asymptotic expansions are obtained for the Pollaczek polynomials Pn(cosθ;a,b). One is for , , in terms of elementary functions and in descending powers of . The other is for , in terms of a special function closely related to the modified parabolic cylinder functions, in descending powers of n. This interval contains a turning point and all possible zeros of Pn(cosθ) in θ(0,π/2]. 相似文献
9.
Let M1 and M2 be two matroids on the same ground set S. We conjecture that if there do not exist disjoint subsets A1,A2,…,Ak+1 of S, such that ispM1(Ai)≠Ø, and similarly for M2, then S is partitioned into k sets, each independent in both M1 and M2. This is a possible generalization of König's edge-coloring theorem. We prove the conjecture for the case k=2 and for a regular case, in which both matroids have the same rank d, and S consists of k·d elements. Finally, we prove another special case related to a conjecture of Rota. 相似文献
10.
Discrete subspaces of countably tight compacta 总被引:1,自引:0,他引:1
Our main result is that the following cardinal arithmetic assumption, which is a slight weakening of GCH, “2κ is a finite successor of κ for every cardinal κ”, implies that in any countably tight compactum X there is a discrete subspace D with . This yields a (consistent) confirmation of Alan Dow’s Conjecture 2 from [A. Dow, Closures of discrete sets in compact spaces, Studia Math. Sci. Hung. 42 (2005) 227–234]. 相似文献
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We work in set-theory without choice ZF. Denoting by the countable axiom of choice, we show in that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p1 (respectively p=0), and some closed subset F of [0,1]I which is a bounded subset of ℓp(I), we show that (respectively DC, the axiom of Dependent Choices) implies the compactness of F. 相似文献
13.
The Padmakar–Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed. Using this formula, the PI indices of C4 nanotubes and nanotori are computed. 相似文献
14.
Recently, it was proved by Leedham-Green and others that with a finite number of exceptions, every p-group of coclass r is a quotient of one of only a finite number of p-adic uniserial space groups. In this paper we use that structure to demonstrate that there are only finitely many isomorphism classes of cohomology rings of 2-groups of coclass r with coefficients in any fixed field k of characteristic 2. In addition, there is experimental evidence indicating that in many cases successive quotients of the uniserial space groups have isomorphic cohomology rings. 相似文献
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In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras. 相似文献
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Covering point sets with two disjoint disks or squares 总被引:1,自引:0,他引:1
Sergio Cabello J. Miguel Díaz-Bez Carlos Seara J. Antoni Sellars Jorge Urrutia Inmaculada Ventura 《Computational Geometry》2008,40(3):195-206
We study the following problem: Given a set of red points and a set of blue points on the plane, find two unit disks CR and CB with disjoint interiors such that the number of red points covered by CR plus the number of blue points covered by CB is maximized. We give an algorithm to solve this problem in O(n8/3log2n) time, where n denotes the total number of points. We also show that the analogous problem of finding two axis-aligned unit squares SR and SB instead of unit disks can be solved in O(nlogn) time, which is optimal. If we do not restrict ourselves to axis-aligned squares, but require that both squares have a common orientation, we give a solution using O(n3logn) time. 相似文献
19.
Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(nlogn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum) area triangle with a vertex at q and the other two vertices in S{q} in optimal O(nlogn) time and O(n) space. Finally, we give an O(nlogn) time, O(n) space algorithm to find the kth closest line from q and show how to find the k closest lines from q in O(nlogn+k) time and O(n+k) space. 相似文献
20.
Let be a dilation-stable process on . We determine a Hausdorff measure function (a) such that the fractal set X[0,1]={X(t):0t1} has positive finite -measure. We also investigate the packing measure of X[0,1]. 相似文献