Journals / Journal of Algebra Combinatorics Discrete Structures and Applications / 2014 / Cilt: 1 - Sayı: 1 #90809
The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes
- Pages
- 13–17
- DOI
- —
Abstract
The existence of a quantum [[28, 12, 6]] code was one of the few cases for codes of length n ≤ 30 thatwas left open in the seminal paper by Calderbank, Rains, Shor, and Sloane [2]. The main result ofthis paper is the construction of the first optimal linear quaternary [28, 20, 6] code which contains itsHermitian dual code and yields the first optimal quantum [[28, 12, 6]] code
Özet
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.