Uniformly Packed Codes and More Distance Regular Graphs from Crooked Functions

Authors:
E. R. Van Dam;D. Fon-Der-Flaass
Affiliations:
Department of Econometrics, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands. edwin.vandam@kub.nl;Institute of Mathematics, Novosibirsk 630090, Russia. d.g.flaass@writeme.com
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2000

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Abstract

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.