II n'y a pas de [q + 1, 2] MDS code cyclique d'ordre impair q

Characterization of $G_2(q)$, where $2 < q equiv 1(mod 3)$ by order components

In this paper we will prove that the simple group $G_2(q)$, where $2 < q equiv 1(mod3)$ is recognizable by the set of its order components, also other word we prove that if $G$ is a finite group with $OC(G)=OC(G_2(q))$, then $G$ is isomorphic to $G_2(q)$.

A study of (x(q + 1), x; 2, q)-minihypers

Constructing new q-ary quantum MDS codes with distances bigger than q/2 from generator matrices

The construction of quantum error-correcting codes has been an active field of quantum information theory since the publication of [1, 2, 3]. It is becoming more and more difficult to construct some new quantum MDS codes with large minimum distance. In this paper, based on the approach developed in the paper [4], we construct several new classes of quantum MDS codes. The quantum MDS codes exhib...

New q-ary quantum MDS codes with distances bigger than \(\frac{q}{2}\)

Constructions of quantum MDS codes have been studied by many authors. We refer to the table in page 1482 of [3] for known constructions. However there have been constructed only a few q-ary quantum MDS [[n, n−2d+2, d]]q codes with minimum distances d > q 2 for sparse lengths n > q + 1. In the case n = q 2 −1 m where m|q + 1 or m|q − 1 there are complete results. In the case n = q 2 −1 m while m...

Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q+1

The entanglement-assisted stabilizer formalism provides a useful framework for constructing quantum error-correcting codes (QECC), which can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this paper, we construct five classes of entanglement-assisted quantum M...