The existence of optimal quaternary $[28,20,6]$ and quantum $[[28,12,6]]$ codes
DOI:
https://doi.org/10.13069/jacodesmath.25090Keywords:
Quantum code, Optimal codeAbstract
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 [2]. 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.
Received: 31 May 2014 | Accepted: 3 August 2014
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