Binary construction of pure additive quantum codes with distance five or six

Binary construction of pure additive quantum codes with distance five or six This paper discusses binary quantum stabilizer codes with distance five or six constructed from binary self-orthogonal codes using Steane construction. First, nineteen special binary one-generator quasi-cyclic self-orthogonal $$[pk,k]$$ [ p k , k ] codes with dual distance five or six for $$12 \le k \le 16$$ 12 ≤ k ≤ 16 are built. Second, a feasible algorithm for searching subcodes of linear codes and an extension strategy for pairs of nested self-orthogonal codes are proposed, then thirty-eight code pairs are designed from obtained quasi-cyclic self-orthogonal codes. Third, thirty-two good binary quantum stabilizer codes are constructed from the code pairs obtained through Steane construction. Thirty of them are previously known codes. In particular, two codes $$[[52,31,6]]$$ [ [ 52 , 31 , 6 ] ] and $$[[56,34,6]]$$ [ [ 56 , 34 , 6 ] ] have improved codes $$[[52,31,5]]$$ [ [ 52 , 31 , 5 ] ] and $$[[56,34,5]]$$ [ [ 56 , 34 , 5 ] ] constructed by quaternary construction, and thus, they are record breaking ones. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Binary construction of pure additive quantum codes with distance five or six

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Publisher
Springer Journals
Copyright
Copyright © 2014 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/s11128-014-0848-1
Publisher site
See Article on Publisher Site

Abstract

This paper discusses binary quantum stabilizer codes with distance five or six constructed from binary self-orthogonal codes using Steane construction. First, nineteen special binary one-generator quasi-cyclic self-orthogonal $$[pk,k]$$ [ p k , k ] codes with dual distance five or six for $$12 \le k \le 16$$ 12 ≤ k ≤ 16 are built. Second, a feasible algorithm for searching subcodes of linear codes and an extension strategy for pairs of nested self-orthogonal codes are proposed, then thirty-eight code pairs are designed from obtained quasi-cyclic self-orthogonal codes. Third, thirty-two good binary quantum stabilizer codes are constructed from the code pairs obtained through Steane construction. Thirty of them are previously known codes. In particular, two codes $$[[52,31,6]]$$ [ [ 52 , 31 , 6 ] ] and $$[[56,34,6]]$$ [ [ 56 , 34 , 6 ] ] have improved codes $$[[52,31,5]]$$ [ [ 52 , 31 , 5 ] ] and $$[[56,34,5]]$$ [ [ 56 , 34 , 5 ] ] constructed by quaternary construction, and thus, they are record breaking ones.

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 15, 2014

References

  • Binary construction of quantum codes of minimum distances five and six
    Li, R; Li, X
  • New quasi-cyclic codes from simplex codes
    Chen, EZ
  • Algebraic structure of quasicyclic codes
    Lally, K; Fitzpatrick, P

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