In this paper we present a class of polynomial primal-dual interior-point algorithms for LO based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai M. El Ghami and C.Roos published in SIAM Journal of Optimization, 13(3):766–782, 2003 [3]. The proposed functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like the usual barrier functions. The goal of this paper is to investigate such class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. The iteration bound of largeupdate interior-point methods based on these functions, are shown to be O n1/1+plog n log n/∈), where p is a parameter, p ∈ [0, 1]. We present also some numerical results which show that by using a new kernel function, the best iteration numbers was achieved in most of the test problems.

The contours of isolated objects in noisy images may be detected with a minimal cost contour detection algorithm. An algorithm that is based on the policy-iteration method for locating the closed minimal cost path is introduced. Computational results indicate that it is computationally more efficient than the dynamic programming approach. The method is applied to left ventricular contours in scintigraphic images, although it is applicable to any domain where a closed minimal cost path is to be computed in a matrix of cost coefficients.>

A new lower bound for the minimum distance of a linear code is derived. When applied to cyclic codes both the Bose-Chaudhuri-Hocquenghem (BCH) bound and the Hartmann-Tzeng (HT) bound are obtained as corollaries. Examples for which the new bound is superior to these two bounds, as well as to the Carlitz-Uchiyama bound, are given.

LetCbe a binary code containing the zero word, with fundamental parametersd,s,d', ands, and lettbe a nonnegative integer such that the words of any fixed weight ofCform at-design, withtmaximal in this respect. It is shown thatt \geq \max(d-s',d'-s). Moreover, ifCcontains the all one word, thent \geq d'- s+1and ifCis an even weight code thent \geq d - s' + 1. Finally, the following inequality is derived:d'-s < d, provided thatd>2.

Algebraic convolutional coding theory is considered. It is shown that any convolutional code has a canonical direct decomposition into subcodes and that this decomposition leads in a natural way to a minimal encoder. Considering cyclic convolutional codes, as defined by Piret, an easy application of the general theory yields a canonical direct decomposition into cyclic subcodes, and at the same time a canonical minimal encoder for such codes. A list of pairs(n,k)admitting completely proper cyclic(n, k)-convolutional codes is included.