A polynomial approach to cocycles over elementary abelian groups

We derive bivariate polynomial formulae for cocycles and coboundaries in Z2(xs2124pn,xs2124pn), and a basis for the (pn-1-n)-dimensional GF(pn)-space of coboundaries. When p=2 we determine a basis for the $(2^n + {n\choose 2} -1)$-dimensional GF(2n)-space of cocycles and show that each cocycle has a unique decomposition as a direct sum of a coboundary and a multiplicative cocycle of restricted form.