Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication
- 주제(키워드) binary linear code , poset , weight distribution , self-orthogonal code , quantum code
- 주제(기타) Mathematics
- 설명문(일반) [Wu, Yansheng] Nanjing Univ Posts & Telecommun, Sch Comp Sci, Nanjing 210023, Peoples R China; [Wu, Yansheng; Lee, Yoonjin] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 gold, Green Submitted
- 발행기관 MDPI
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000174551
- 본문언어 영어
- Published As http://dx.doi.org/10.3390/math8091495
초록/요약
It is an important issue to search for self-orthogonal codes for construction of quantum codes byCSS construction(Calderbank-Sho-Steane codes); in quantum error correction,CSS codesare a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these self-orthogonal codes for obtaining binary quantum codes. Finally, we obtain four infinite families of binary quantum codes for which the minimum distances are three or four by CSS construction, which include binary quantum Hamming codes with length n >= 7. We also find some (almost) "optimal" quantum codes according to the current database of Grassl. Furthermore, we explicitly determine the weight distributions of these linear codes constructed using posets, and we present two infinite families of some optimal binary linear codes with respect to the Griesmer bound and a class of binary Hamming codes.
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