  The Equivalence Theorem states that, for a given weight on the alphabet,
every linear isometry between linear codes extends to a monomial transformation
of the entire space. This theorem has been proved for several weights and
alphabets, including the original MacWilliams' Equivalence Theorem for the
Hamming weight on codes over finite fields. The question remains: What
conditions must a weight satisfy so that the Extension Theorem will hold? In
this paper we provide an algebraic framework for determining such conditions,
generalising the approach taken in [Greferath, Honold '06].
