Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

This article reviews some of the principal and recently-discovered lower and upper bounds
on the maximum size of (n, r)-arcs in PG (2, q), sets of n points with at most r points on a line …

In this paper we construct constant dimension codes with prescribed minimum distance.
There is an increased interest in subspace codes in general since a paper [13] by Kötter and …

Finite Geometries stands out from recent textbooks about the subject of finite geometries by
having a broader scope. The authors thoroughly explain how the subject of finite geometries …

We construct new linear two-weight codes over the finite field with q elements. To do so we
solve the equivalent problem of finding point sets in the projective geometry with certain …

It is shown that the parameters of a linear code over \mathbbF_q of length n, dimension k,
minimum weight d, and maximum weight m satisfy a certain congruence relation. In the case …

New linear codes (sometimes optimal) over the finite field with q elements are constructed.
In order to do this, an equivalence between the existence of a linear code with a prescribed …

Abstract In 1986, Kreher and Radziszowski were the first who used the famous LLL
algorithm to construct combinatorial designs. Subsequently, lattice algorithms have been …

Abstract An (n, r)-arc is a set of n points of a projective plane such that some r but no r+ 1 of
them are collinear. The maximum size of an (n, r)-arc in PG (2, q) is denoted by mr (2, q). In …

The main purpose of this paper is to find double blocking sets in PG (2, q) of size less than 3
q, in particular when q is prime. To this end, we study double blocking sets in PG (2, q) of …