A New Construction of Group and Nongroup Perfect Codes

From two perfect 1-codes C ′ and C ′′ in cartesian products S ′ respective S ′′ we shall construct a perfect 1-code C in a cartesian product S . We shall show how the codes C ′ and C ′′ might be chosen so that the code C will be equivalent respective not equivalent to a subgroup of S . We shall also give an example of a perfect 1-code that is not equivalent to any “Vasilev” code.