Let A_ {R, q} denote a family of covering codes, in which the covering radius R and the size
q of the underlying Galois field are fixed, while the code length tends to infinity. In this paper …

The defect of an linear code is defined as. Codes with are called maximum distance
separable (MDS), while codes with are called near maximum distance separable (NMDS) …

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 …

In the projective space PG (k− 1, q) over Fq, the finite field of order q, an (n; r)-arc K is a set of
n points with at most r on a hyperplane and there is some hyperplane meeting K in exactly r …

Grassmannian G _q (n, k) G q (n, k) is the set of all k-dimensional subspaces of the vector
space F _q^ n F qn. Kötter and Kschischang showed that codes in Grassmannian space can …

An arc and a blocking set are both geometrical objects linked with linear codes. In this
paper, we use relations among these objects to prove the non-existence of linear codes over …

The aim of the paper is to compute projective maximum distance separable codes,-MDS of
two and three dimensions with certain lengths and Hamming weight distribution from the …

In this paper we give a geometrical construction of a (56, 2)-blocking set in PG (2, 19) and
We obtain a new (325, 18)-arc and a new linear code and apply the Grismer rule so that we …

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 …

Near-MDS have been introduced in 1995 in [11]. They are defined by weakening some
restrictions in the definition of the MDS codes. The most popular definition is via generalized …