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

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
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/s11128-016-1320-1
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

References

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