Polynomial invariants of quantum codes

The weight enumerators [8] of a quantum code are quite powerful tools for e xploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher degree polynomial in variants, We show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one-to-one correspondence wit h S-k(n). We then present a number of equations and inequalities in these i nvariants; in particular, we give a higher order generalization of the shad ow enumerator of a code, and prove that its coefficients are nonnegative. W e also prove that the quartic invariants of a ((4, 4, 2))(2) code are uniqu ely determined, an important step in a proof that any ((4, 4, 2))(2) code i s additive [6].