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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 derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n.

A graph G is called bisectable if it is an edge-disjoint union of two isomorphic subgraphs. We show that any tree T with e edges contains a bisectable subgraph with at least e-O(e/log log e) edges. We also show that every forest of size e, each component of which is a star, contains a bisectable subgraph of size at least e-O(log2 e).

We derive new conditions for nonexistence of integral zeros of binary Kraw-tchouk polynomials. Upper bounds for the number of integral roots of Kraw-tchouk polynomials are presented.

Abstruct-We derive an estimate for the error term in the binomial approximation of spectra of BCH codes. This estimate asymptotically improves on the earlier hounds

A general technique for tackling various reconstruction problems is presented and applied to some old and some new instances of such problems.

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)