On perfect codes over non prime power alphabets

Known results on perfect codes over alphabets with q elements where q is not a prime power is surveyed. Some tools recently developed for the study of perfect 1-error correcting binary codes are generalized to the case of non prime power alphabets. A theorem by H. W. Lenstra from 1972 on the algebraic structure of perfect codes over non prime power alphabets will, by using this generalization, be further strengthened.