Divisibility of Weights for Ideals in Group Algebras

In this short note we clarify some questions on the greatest common divisor of all weights of a group code. In particular we discuss Ward’s condition (E) in Ward, H. (Q. J. Math. Oxford 34 , 115–128, 1983 ) and extend a result of Damgård and Landrock on the principal block to self-dual blocks. Furthermore, we give an upper bound for the dimension of a group code in terms of its monomial kernel.