Some Results on Difference Balanced Functions

Conference paper

DOI: 10.1007/978-3-319-16277-5_6

Volume 9061 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Pott A., Wang Q. (2015) Some Results on Difference Balanced Functions. In: Koç Ç., Mesnager S., Savaş E. (eds) Arithmetic of Finite Fields. WAIFI 2014. Lecture Notes in Computer Science, vol 9061. Springer, Cham

Abstract

For a difference balanced function \(f\) from \({\mathbb F}_{q^n}^*\) to \({\mathbb F}_q\), the set \(D := \{ (x, f(x)) : x \in {\mathbb F}_{q^n}^* \}\) is a generalized difference set with respect to two exceptional subgroups \(({\mathbb F}_{q^n}^*, \cdot )\) and \(({\mathbb F}_q, +)\). This allows us to prove the balance property of difference balanced functions from \({\mathbb F}_{q^n}^*\) to \({\mathbb F}_q\) where \(q\) is a prime power. We further prove two necessary and sufficient conditions for \(d\)-homogeneous difference balanced functions. This unifies several combinatorial objects related to difference balanced functions.

Keywords

Difference balanced function \(d\)-homogeneous function Generalized difference set \(p\)-ary sequence with ideal autocorrelation Two-tuple balanced function 

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics, Institute of Algebra and GeometryOtto-von-Guericke University MagdeburgMagdeburgGermany
  2. 2.Department of Electrical and Electronic EngineeringSouth University of Science and Technology of ChinaNanshan ShenzhenChina