Higher-spin fields and charges in the periodic spinor space

The $sp(2M)$ invariant unfolded system is considered in the periodic twistor-like spinor space. Complete set of non-trivial charges corresponding to the global symmetry compatible with the periodicity conditions is constructed. Residual infinite-dimensional symmetry is realized in terms of the star-product algebra. It is shown that charges associated with integrations over different cycles are related by particular higher-spin symmetry transformations.