Abstract

A construction of perfect binary codes is presented. It is shown that this construction gives rise to perfect codes that are nonequivalent to any of the previously known perfect codes. Furthermore, perfect codes C 1 and C 2 are constructed such that their intersection C 1∩C 2 has the maximum possible cardinality. The latter result is then employed to explicitly construct 22cn nonequivalent perfect codes of length n, for sufficiently large n and some constant c slightly less than 0.5.KeywordsParity CheckParity Check MatrixCoset RepresentativePerfect CodePerfect SegmentationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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