The existence of optimal quaternary [28, 20, 6] and quantum [[28, 12, 6]] codes

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

Keywords

• Quantum code
• Optimal code
• quaternary

The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes

Öz

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.

Anahtar Kelimeler

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Kaynakça

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4. M. Grassl, http://www.codetables.de.
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