2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90571This paper is motivated by the computer-generated nonadditive ((5,6,2)) code described in an article by Rains, Hardin, Shor and Sloane. We describe a theory of non-stabilizer codes of which the nonadditive code of Rains et al is an example. Furthermore, we give a general strategy of constructing good nonstabilizer codes from good stabilizer codes and give some explicit constructions and asymptotically good nonstabilizer codes. In fact, we explicitly construct a family of distance 2 non-stabilizer codes over all finite fields of which the ((5,6,2)) is an special example. More interestingly, using our theory, we are also able to explicitly construct examples of non-stablizer quantum codes of distance 3. Like in the case of stabilizer codes, we can design fairly efficient encoding and decoding procedures.29 pages, latex file with 6 figures as pstex and pstex_t filesQuantum Physicstext