WAIFI 2007: Arithmetic of Finite Fields pp 11-17

# Some Notes on d-Form Functions with Difference-Balanced Property

• Tongjiang Yan
• Xiaoni Du
• Enjian Bai
• Guozhen Xiao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)

## Abstract

The relation between a cyclic relative difference set and a cyclic difference set is considered. Both the sets are with Singer parameters and can be constructed from a difference-balanced d-form function. Although neither of the inversions of Klapper A.′s and No J. S.′s main theorems is true, we prove that a difference-balanced d-form function can be obtained by the cyclic relative difference set and the cyclic difference set introduced by these two main theorems respectively.

## Keywords

Cyclic difference sets cyclic relative difference sets d-form functions difference-balanced

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## Authors and Affiliations

• Tongjiang Yan
• 1
• 2
• Xiaoni Du
• 2
• 4
• Enjian Bai
• 3
• Guozhen Xiao
• 2
1. 1.Math. and Comp. Sci., China Univ. of Petro., Dongying 257061China
2. 2.P.O.Box 119, Key Lab.on ISN, Xidian Univ., Xi’an 710071China
3. 3.Inform. Sci. and Tech., Donghua Univ., Shanghai 201620China
4. 4.Math. and Inform. Sci, Northwest Normal Univ., Lanzhou 730070China