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

Source abstract

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