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New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions

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Abstract

In this paper, for a prime power q, new cyclic difference sets with Singer para- meters ((q n−1/q−1), (q n−1−1/q−1), (q n−2−1/q−1)) are constructed by using q-ary sequences (d-homogeneous functions) of period q n−1 and the generalization of GMW difference sets is proposed by combining the generation methods of d-form sequences and extended sequences. When q is a power of 3, new cyclic difference sets with Singer parameters ((q n−1/q−1), (q n−1−1/q−1), (q n−2−1/q−1)) are constructed from the ternary sequences of period q n−1 with ideal autocorrelation introduced by Helleseth, Kumar, and Martinsen.

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  1. Jong-Seon No
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No, JS. New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions. Designs, Codes and Cryptography 33, 199–213 (2004). https://doi.org/10.1023/B:DESI.0000036246.52472.81

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