Paper Info
Title
A Construction of New Quantum MDS Codes
Abstract
It has been a great challenge to construct new quantum maximum-distance-separable (MDS) codes. In particular, it is very hard to construct the quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known q-ary quantum MDS codes have minimum distance ≤q/2 + 1. In this paper, we provide a construction of the quantum MDS codes with minimum distance >q/2 + 1. In particular, we show the existence of the q-ary quantum MDS codes with length n = q2 + 1 and minimum distance d for any d q + 1 (this result extends those given in the works of Guardia (2011), Jin et al. (2010), and Kai an Zhu (2012)); and with length (q2 + 2)/3 and minimum distance d for any d (2q+2)/3 if 3|(q + 1). Our method is through Hermitian selforthogonal codes. The main idea of constructing the Hermitian self-orthogonal codes is based on the solvability in Fq of a system of homogenous equations over Fq2.
Year
DOI
Venue
2013
10.1109/TIT.2014.2299800
IEEE Transactions on Information Theory
Keywords
DocType
Volume
mds codes,quantum maximum distance separable codes,minimum distance,hermitian self-orthogonal codes,codes,self-orthogonal,quantum computing,generalized reed-solomon codes,quantum codes,hermitian inner product,quantum mds codes,maximum-distance-separable (mds) codes,quantum mechanics,vectors
Journal
60
Issue
ISSN
Citations 
5
0018-9448
19
PageRank 
References 
Authors
0.88
13
2
Name
Order
Citations
PageRank
Lingfei Jin113515.30
Chaoping Xing2916110.47