Let K be a dyadic local
field, o its ring of integers, L a regular unimodular lattice over o. If x and y are
vectors in L, we ask for necessary and sufficient conditions to map x isometrically to
y. Trojan and James obtain conditions via a T-invariant when o is 2-adic. Hsia uses
characteristic sets and G-invariants for vectors and he solves the problem when o is
dyadic in general. We define here a new numerical invariant, the degree of
a vector, which reflects more on the structure of L and the relationship
between x, y and L. The Witt conditions will be stated in terms of this degree
invariant.
