turkmath.org

This talk covers basics of error correcting codes and codes over local Frobenius rings of order 16 and their images to the binary space via a Gray map which need not be linear. We define Lee weight based on the Hamming weight of the Gray image. This Gray map is a canonical extension of the usual Gray maps as defined over local rings of order 4 and it is presented in a very general form which can be applied to any local Frobenius ring of order 16 with a maximal ideal of size 8. We construct self-dual codes over these rings and give their binary images.