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Codes as fractals and noncommutative spaces (1107.5782v1)
Published 28 Jul 2011 in cs.IT and math.IT
Abstract: We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can associate geometric spaces constructed using methods from noncommutative geometry, arising from rational noncommutative tori and finite abelian group actions on Cuntz algebras and fractals associated to the classical codes.