New optimal subsystem codes

Subsystem codes (also known as operator quantum error-correcting codes) are a generalization of noiseless subsystems, decoherence-free subspaces, and quantum error-correcting codes. In this note, we present a construction for new subsystem codes with parameters [ [ q 2 + 1 , ( q − 1 ) 2 , 4 , q − 1 ] ] q , where q = 2 m , and m ≥ 1 is a positive integer, whose parameters are not covered by the codes available in the literature. Moreover, the constructed subsystem codes are optimal.