# Improved constructions for quantum maximum distance separable codes

Improved constructions for quantum maximum distance separable codes In this work, we further improve the distance of the quantum maximum distance separable (MDS) codes of length $$n=\frac{q^2+1}{10}$$ n = q 2 + 1 10 . This yields new families of quantum MDS codes. We also construct a family of new quantum MDS codes with parameters $$[[\frac{q^2-1}{3}, \frac{q^2-1}{3}-2d+2, d]]_{q}$$ [ [ q 2 - 1 3 , q 2 - 1 3 - 2 d + 2 , d ] ] q , where $$q=2^m$$ q = 2 m , $$2\le d\le \frac{q-1}{3}$$ 2 ≤ d ≤ q - 1 3 if $$3\mid (q+2)$$ 3 ∣ ( q + 2 ) , and $$2\le d\le \frac{2q-1}{3}$$ 2 ≤ d ≤ 2 q - 1 3 if $$3\mid (q+1)$$ 3 ∣ ( q + 1 ) . Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Improved constructions for quantum maximum distance separable codes

, Volume 16 (1) – Dec 18, 2016
10 pages

/lp/springer_journal/improved-constructions-for-quantum-maximum-distance-separable-codes-hChNpqfLLe
Publisher
Springer Journals
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/s11128-016-1490-x
Publisher site
See Article on Publisher Site

### Abstract

In this work, we further improve the distance of the quantum maximum distance separable (MDS) codes of length $$n=\frac{q^2+1}{10}$$ n = q 2 + 1 10 . This yields new families of quantum MDS codes. We also construct a family of new quantum MDS codes with parameters $$[[\frac{q^2-1}{3}, \frac{q^2-1}{3}-2d+2, d]]_{q}$$ [ [ q 2 - 1 3 , q 2 - 1 3 - 2 d + 2 , d ] ] q , where $$q=2^m$$ q = 2 m , $$2\le d\le \frac{q-1}{3}$$ 2 ≤ d ≤ q - 1 3 if $$3\mid (q+2)$$ 3 ∣ ( q + 2 ) , and $$2\le d\le \frac{2q-1}{3}$$ 2 ≤ d ≤ 2 q - 1 3 if $$3\mid (q+1)$$ 3 ∣ ( q + 1 ) . Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 18, 2016

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