Ilia Krasikov

Learn More
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)