Introduction to Coding Theory
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This paper is motivated by the computer-generated nonadditive code describedin Rains et al [1]. We describe a theory of non-stabilizer codes of which thenonadditive code of Rains et al is an example. Furthermore, we give a general strategyof constructing good nonstabilizer codes from good stabilizer codes and give someexplicit constructions and asymptotically good nonstabilizer codes. Like in the case ofstabilizer codes, we can design fairly efficient encoding and decoding procedures.