# 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 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/s11128-016-1490-x
Publisher site
See Article on Publisher Site

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial