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

Vladimir D. Tonchev

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 \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.

Keywords


Quantum code, Optimal code

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ISSN: 2148-838X