# New asymmetric quantum codes over $$F_{q}$$ F q

New asymmetric quantum codes over $$F_{q}$$ F q Two families of new asymmetric quantum codes are constructed in this paper. The first family is the asymmetric quantum codes with length $$n=q^{m}-1$$ n = q m - 1 over $$F_{q}$$ F q , where $$q\ge 5$$ q ≥ 5 is a prime power. The second one is the asymmetric quantum codes with length $$n=3^{m}-1$$ n = 3 m - 1 . These asymmetric quantum codes are derived from the CSS construction and pairs of nested BCH codes. Moreover, let the defining set $$T_{1}=T_{2}^{-q}$$ T 1 = T 2 - q , then the real Z-distance of our asymmetric quantum codes are much larger than $$\delta _\mathrm{max}+1$$ δ max + 1 , where $$\delta _\mathrm{max}$$ δ max is the maximal designed distance of dual-containing narrow-sense BCH code, and the parameters presented here have better than the ones available in the literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# New asymmetric quantum codes over $$F_{q}$$ F q

Quantum Information Processing, Volume 15 (7) – Apr 26, 2016
11 pages

/lp/springer-journals/new-asymmetric-quantum-codes-over-f-q-f-q-UqoQrLmzjL
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
DOI
10.1007/s11128-016-1320-1
Publisher site
See Article on Publisher Site

### Abstract

Two families of new asymmetric quantum codes are constructed in this paper. The first family is the asymmetric quantum codes with length $$n=q^{m}-1$$ n = q m - 1 over $$F_{q}$$ F q , where $$q\ge 5$$ q ≥ 5 is a prime power. The second one is the asymmetric quantum codes with length $$n=3^{m}-1$$ n = 3 m - 1 . These asymmetric quantum codes are derived from the CSS construction and pairs of nested BCH codes. Moreover, let the defining set $$T_{1}=T_{2}^{-q}$$ T 1 = T 2 - q , then the real Z-distance of our asymmetric quantum codes are much larger than $$\delta _\mathrm{max}+1$$ δ max + 1 , where $$\delta _\mathrm{max}$$ δ max is the maximal designed distance of dual-containing narrow-sense BCH code, and the parameters presented here have better than the ones available in the literature.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Apr 26, 2016

## 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 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### 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. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create folders to

Export folders, citations