On the p-Ranks and Characteristic Polynomials of Cyclic Difference Sets

Authors:
Jong-seon No;Dong-joon Shin;Tor Helleseth
Affiliations:
School of Electrical Engineering and Computer Science, Seoul National University, Seoul 151-742, Korea;Division of Electrical and Computer Engineering, Hanyang University, Seoul 133-791, Korea;Department of Informatics, University of Bergen, N-5020 Bergen, Norway
Venue:
Designs, Codes and Cryptography
Year:
2004

Citing 8
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Abstract

In this paper, the p-ranks and characteristic polynomials of cyclic difference sets are derived by expanding the trace expressions of their characteristic sequences. Using this method, it is shown that the 3-ranks and characteristic polynomials of the Helleseth–Kumar–Martinsen (HKM) difference set and the Lin difference set can be easily obtained. Also, the p-rank of a Singer difference set is reviewed and the characteristic polynomial is calculated using our approach.