The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes
The existence of a quantum $[[28,12,6]]$ code was one of the few cases for codes of length $n\le 30$ that was left open in the seminal paper by Calderbank, Rains, Shor, and Sloane \cite{CRSS}. The main result of this paper is the construction of a new optimal linear quaternary $[28,20,6]$ code which...
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Yildiz Technical University
2014-09-01
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| Series: | Journal of Algebra Combinatorics Discrete Structures and Applications |
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| Online Access: | http://www.eds.yildiz.edu.tr/AjaxTool/GetArticleByPublishedArticleId?PublishedArticleId=2028 |
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doaj-788017402f1840d6be313ec3b4d3dbdd2020-11-25T00:33:06ZengYildiz Technical UniversityJournal of Algebra Combinatorics Discrete Structures and Applications2148-838X2014-09-01111317The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes Vladimir D. Tonchev 0Michigan Technological UniversityThe existence of a quantum $[[28,12,6]]$ code was one of the few cases for codes of length $n\le 30$ that was left open in the seminal paper by Calderbank, Rains, Shor, and Sloane \cite{CRSS}. The main result of this paper is the construction of a new optimal linear quaternary $[28,20,6]$ code which contains its hermitian dual code and yields an optimal linear quantum $[[28,12,6]]$ code.http://www.eds.yildiz.edu.tr/AjaxTool/GetArticleByPublishedArticleId?PublishedArticleId=2028Quantum codeOptimal code |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Vladimir D. Tonchev |
| spellingShingle |
Vladimir D. Tonchev The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes Journal of Algebra Combinatorics Discrete Structures and Applications Quantum code Optimal code |
| author_facet |
Vladimir D. Tonchev |
| author_sort |
Vladimir D. Tonchev |
| title |
The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes |
| title_short |
The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes |
| title_full |
The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes |
| title_fullStr |
The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes |
| title_full_unstemmed |
The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes |
| title_sort |
existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes |
| publisher |
Yildiz Technical University |
| series |
Journal of Algebra Combinatorics Discrete Structures and Applications |
| issn |
2148-838X |
| publishDate |
2014-09-01 |
| description |
The existence of a quantum $[[28,12,6]]$ code was one of the few cases for codes of length $n\le 30$ that was left open in the seminal paper by Calderbank, Rains, Shor, and Sloane \cite{CRSS}. The main result of this paper is the construction of a new optimal linear quaternary $[28,20,6]$ code which contains its hermitian dual code and yields an optimal linear quantum $[[28,12,6]]$ code. |
| topic |
Quantum code Optimal code |
| url |
http://www.eds.yildiz.edu.tr/AjaxTool/GetArticleByPublishedArticleId?PublishedArticleId=2028 |
| work_keys_str_mv |
AT vladimirdtonchev theexistenceofoptimalquaternary28206andquantum28126codes AT vladimirdtonchev existenceofoptimalquaternary28206andquantum28126codes |
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