A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

Authors:
K. T. Arasu;Kevin J. Player
Affiliations:
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, U.S.A.;Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, U.S.A.
Venue:
Designs, Codes and Cryptography
Year:
2003

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Abstract

We construct a new family of cyclic difference sets with parameters ((3d − 1)/2, (3d − 1 − 1)/2, (3d − 2 − 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.