Linear spaces with many small lines

Linear spaces with many small lines

In this paper some of the work in linear spaces in which most of the lines have few points is surveyed. This includes existence results, blocking sets and embeddings. Also, it is shown that any linear space of order c can be embedded in a linear space of order about 13v in which there are no lines of size 2.

On some finite linear spaces with few lines

Banach Spaces with Many Projections

A fundamental question in operator theory is: how rich is the collection of oprrators on a given Banach space? For classical spaces, especially Hilbert space, a well developed theory of operators exists. However a Banach space may have far fewer operators than one might expect. Shelah [S] has constructed a nonseparable Ba~lach space X , for which the space of operators with separable range has ...

On Linear Cryptanalysis with Many Linear Approximations

In this paper we present a theoretical framework to quantify the information brought by several linear approximations of a blockcipher without putting any restriction on these approximations. We quantify here the entropy of the key given the plaintext-ciphertext pairs statistics which is a much more accurate measure than the ones studied earlier. The techniques which are developed here apply to...

Sets of Points with Many Halving Lines

We used a genetic search algorithm to find sets of points with many halving lines. There are sets of 10 points with 13 halving lines, 12 points with 18 halving lines, 14 points with 22 halving lines, 16 points with 27 halving lines, and 18 points with 32 halving lines. We find a construction generalizing the 12 point configuration and show that, for any n = 3 · 2, there are configurations of n ...