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- Title
Ternary optimal quantum codes constructed from caps in PG(k,9)(k≥2).
- Authors
Li, Husheng; Li, Ruihu; Fu, Qiang; Zhan, Xiuzhen
- Abstract
By recursive construction and computer-supported search method, the spectrum of quantum caps in projective space P G (k , 9) (k ≥ 2) is determined. Through Hermitian construction, the obtained quantum caps are used to construct ternary quantum codes of d = 4 . As a result, for each integer n satisfying n ≥ 10 , a quantum n-cap in P G (k - 1 , 9) with suitable k and its related ternary [ [ n , n - 2 k , 4 ] ] quantum code are constructively proven to exist. According to quantum GV bound and quantum Hamming bound, all quantum codes are optimal. In addition, while constructing quantum caps, the cardinalities of maximal caps in PG(7, 9) and PG(8, 9) are also improved.
- Subjects
INTEGERS
- Publication
Quantum Information Processing, 2022, Vol 21, Issue 3, p1
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-022-03437-5