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We construct canonical frames and find all maximally symmetric models for anatural generic class of corank 2 distributions on manifolds of odd dimensiongreater or equal to 7. This class of distributions is characterized by thefollowing two conditions: the pencil of 2-forms associated with thecorresponding Pfaffian system has the maximal possible first Kronecker indexand the Lie square of the subdistribution generated by the kernels of all these2-forms is equal to the original distribution. In particular, we show that theunique, up to a local equivalence, maximally symmetric model in this class ofdistributions with given dimension of the ambient manifold exists if and onlyif the dimension of the ambient manifold is equal to 7, 9, 11, 15 or 8l-3,where $l$ is an arbitrary natural number. Besides, if the dimension of theambient manifold is equal to 19, then there exist two maximally symmetricmodels, up to a local equivalence, distinguished by certain discrete invariant.For all other dimensions of ambient manifold there are families of maximallysymmetric models, depending on continuous parameters. Our main tool is theso-called symplectification procedure having its origin in Optimal ControlTheory. Our results can be seen as an extension of some classical Cartan'sresults about rank 3 distributions on a 5-dimensional manifold to corank 2distributions of higher odd rank.

Canonical frames for distributions of odd rank and corank 2 with maximal first Kronecker index