Open AccessThe existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes
Author(s) -
Vladimir D. Tonchev
Publication year - 2014
Publication title -
journal of algebra combinatorics discrete structures and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.137
H-Index - 1
ISSN - 2148-838X
DOI - 10.13069/jacodesmath.25090
Subject(s) - quaternary , quantum , mathematics , theoretical physics , physics , geology , quantum mechanics , paleontology
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom