2 research outputs found
MDS codes with arbitrary dimensional hull and their applications
The hull of linear codes have promising utilization in coding theory and
quantum coding theory. In this paper, we study the hull of generalized
Reed-Solomon codes and extended generalized Reed-Solomon codes over finite
fields with respect to the Euclidean inner product. Several infinite families
of MDS codes with arbitrary dimensional hull are presented. As an application,
using these MDS codes with arbitrary dimensional hull, we construct several new
infinite families of entanglement-assisted quantum error-correcting codes with
flexible parameters.Comment: 17 pages, 1 figur
Constructions of quantum MDS codes
Let be a finite field with elements, where is a
prime number and is an integer. In this paper, by means of
generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum
maximum-distance-separable ( quantum MDS) codes with parameters
for , and for and . Our constructions improve and generalize some results of
available in the literature. Moreover, we give an affirmative answer to the
open problem proposed by Fang et al. in \cite{Fang1}.Comment: 10 pages,2 table