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 [[q2+1,(q−1)2,4,q−1]]q, where q=2m, 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.