A Classification of Additive Symmetric 2-cocycles

We present a classification of the so-called “additive symmetric 2-cocycles” of arbitrary degree and dimension over Fp, along with a partial result and some conjectures for m-cocycles over Fp, m> 2. This expands greatly on a result originally due to Lazard and more recently investigated by Ando, Hopkins and Strickland, and together with their work this culminates in a complete classification of 2-cocycles over an arbitrary commutative ring. The ring classifying these polynomials finds application in algebraic topology, to be fully explored in a sequel.