Construction of Optimal Linear Codes Using Flats and Spreads in a Finite Projective Geometry

In this paper, we shall consider a problem of constructing an optimal linear code whose code length n is minimum among (*, k, d ; s)-codes for given integers k, d and s. In [5], we showed that this problem is equivalent to Problem B of a linear programming which has some geometrical structure and gave a geometrical method of constructing a solution of Problem B using a set of flats in a finite projective geometry and obtained a necessary and sufficient conditions for integers k, d and s that there exists such a geometrical solution of Problem B for given integers k, d and s. But there was no space to give the proof of the main theorem 4.2 in [5]. The purpose of this paper is to give the proof of [5, Theorem 4.2], i.e. to give a systematic method of constructing a solution of Problem B using flats and spreads in a finite projective geometry

On an interpolation using Taylor expansion

In [3] and [4], we obtained the ten-node interpolation and the twelve-node interpolation using Taylor expansion, respectively. In the present paper, we shall show interpolation formulas from two-node to thirteen-node excepting ten-node and twelve-node, using Taylor expansion by the same method in [3] and [4]

On a new multistep method III

In [2], we used the fourth order Bessel central difference formula to cut the step size in half, for the first approximate value of middle value. However, the corrections by correctors have big errors. For this reason, we did not write numerical example for initial value problems of differential equations. But fortunately we have obtained the ten-node interpolation using Taylor expansion, and the twelve-node interpolation using Taylor expansion in [3] and [4], respectively. So we shall show numerical examples for initial problems of differential equations

Infty- an integrated OCR system for mathematical documents

An integrated OCR system for mathematical documents, called INFTY, is presented. INFTY consists of four procedures, i.e., layout analysis, character recognition, structure analysis of mathematical expressions, and manual error correction. In those procedures, several novel techniques are utilized for better recognition performance. Experimental results on about 500 pages of mathematical documents showed high character recognition rates on both mathematical expressions and ordinary texts, and sufficient performance on the structure analysis of the mathematical expressions