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Journals and Conferences
Let X be a (finite or infinite) set and let G be a (finite or infinite) group of automorphisms of X. Thus G acts on X and for every g E G the sequence k&x is a permutation of X. For every subset Y of X and every g E G, let g Y be the set of all elements gy, for y E Y. Clearly 1 g Y 1 = 1 Y 1 for every finite Y, and this defines an action of the group G on… (More)
We study the problem of finding the next-to-shortest paths in a graph. A next-to-shortest (u, v)-path is a shortest (u, v)-path amongst (u, v)paths with length strictly greater than the length of the shortest (u, v)path. In constrast to the situation in directed graphs, where the problem has been shown to be NP-hard, providing edges of length zero are… (More)
We estimate the interval where the distance distribution of a code of length n and of given dual distance is upperbounded by the binomial distribution. The binomial upper bound is shown to be sharp in this range in the sense that for every subinterval of size about p n ln n there exists a spectrum component asymptotically achieving the binomial bound. For… (More)
We derive a new upper bound on the minimum distance of doubly-even self-dual codes of length . Asymptotically, for growing, it gives lim sup (5 5 ) 10
We shall establish two-side explicit inequalities, which are asymptotically sharp up to a constant factor, on the maximum value of |Hk(x)|e −x2/2, on the real axis, where Hk are the Hermite polynomials.
For ν > −1/2 and x real we shall establish explicit bounds for the Bessel function Jν(x) which are uniform in x and ν. This work and the recent result of L. J. Landau  provide relatively sharp inequalities for all real x.
We derive new conditions for nonexistence of integral zeros of binary Krawtchouk polynomials. Upper bounds for the number of integral roots of Krawtchouk polynomials are presented.