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Self-dual, dual-containing and related quantum codes from group rings (0711.3983v1)
Published 26 Nov 2007 in cs.IT, math.IT, and math.RA
Abstract: Classes of self-dual codes and dual-containing codes are constructed. The codes are obtained within group rings and, using an isomorphism between group rings and matrices, equivalent codes are obtained in matrix form. Distances and other properties are derived by working within the group ring. Quantum codes are constructed from the dual-containing codes.