# New quantum MDS codes derived from constacyclic codes

New quantum MDS codes derived from constacyclic codes Quantum maximum-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we construct two classes of quantum MDS codes with parameters \begin{aligned}{}[[\lambda (q-1),\lambda (q-1)-2d+2,d]]_q \end{aligned} [ [ λ ( q - 1 ) , λ ( q - 1 ) - 2 d + 2 , d ] ] q where $$2\le d\le (q+1)/2+\lambda -1$$ 2 ≤ d ≤ ( q + 1 ) / 2 + λ - 1 , and $$q+1=\lambda r$$ q + 1 = λ r with $$r$$ r even, and \begin{aligned}{}[[\lambda (q-1),\lambda (q-1)-2d+2,d]]_q \end{aligned} [ [ λ ( q - 1 ) , λ ( q - 1 ) - 2 d + 2 , d ] ] q where $$2\le d\le (q+1)/2+\lambda /2-1$$ 2 ≤ d ≤ ( q + 1 ) / 2 + λ / 2 - 1 , and $$q+1=\lambda r$$ q + 1 = λ r with $$r$$ r odd. The quantum MDS codes exhibited here have parameters better than the ones available in the literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# New quantum MDS codes derived from constacyclic codes

, Volume 14 (3) – Jan 7, 2015
9 pages

/lp/springer_journal/new-quantum-mds-codes-derived-from-constacyclic-codes-FaXFQ0zGaC
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0903-y
Publisher site
See Article on Publisher Site

### Abstract

Quantum maximum-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we construct two classes of quantum MDS codes with parameters \begin{aligned}{}[[\lambda (q-1),\lambda (q-1)-2d+2,d]]_q \end{aligned} [ [ λ ( q - 1 ) , λ ( q - 1 ) - 2 d + 2 , d ] ] q where $$2\le d\le (q+1)/2+\lambda -1$$ 2 ≤ d ≤ ( q + 1 ) / 2 + λ - 1 , and $$q+1=\lambda r$$ q + 1 = λ r with $$r$$ r even, and \begin{aligned}{}[[\lambda (q-1),\lambda (q-1)-2d+2,d]]_q \end{aligned} [ [ λ ( q - 1 ) , λ ( q - 1 ) - 2 d + 2 , d ] ] q where $$2\le d\le (q+1)/2+\lambda /2-1$$ 2 ≤ d ≤ ( q + 1 ) / 2 + λ / 2 - 1 , and $$q+1=\lambda r$$ q + 1 = λ r with $$r$$ r odd. The quantum MDS codes exhibited here have parameters better than the ones available in the literature.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 7, 2015

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