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Let iV and iW be in-dimensional vector spaces over GF(2). A function iQ : iV → iW is called icrooked (a notion introduced by Bending and Fon-Der-Flaass) if it satisfies the following three properties:We show that crooked functions can be used to construct distance regular graphs with parameters of a Kasami distance regular graph, symmetric 5-class association schemes similar to those recently constructed by de Caen and van Dam from Kasami graphs, and uniformly packed codes with the same parameters as the double error-correcting BCH codes and Preparata codes.

Uniformly Packed Codes and More Distance Regular Graphs from Crooked Functions