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International Workshop on the Arithmetic of Finite Fields

WAIFI 2014: Arithmetic of Finite Fields pp 111–120Cite as

Some Results on Difference Balanced Functions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9061))

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.

The work was partially done when the second author was working at Institute of Algebra and Geometry, Otto-von-Guericke University Magdeburg, Magdeburg, Germany, supported by the Alexander von Humboldt Foundation.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Institute of Algebra and Geometry, Otto-von-Guericke University Magdeburg, 39106, Magdeburg, Germany

    Alexander Pott

  2. Department of Electrical and Electronic Engineering, South University of Science and Technology of China, Nanshan Shenzhen, 518055, Guangdong, China

    Qi Wang

Authors
  1. Alexander Pott
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  2. Qi Wang
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Corresponding author

Correspondence to Qi Wang .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Univ of California, Santa Barbara, Santa Barbara, California, USA

    Çetin Kaya Koç

  2. University of Paris VIII, Paris, France

    Sihem Mesnager

  3. Sabancı University, Istanbul, Turkey

    Erkay Savaş

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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. https://doi.org/10.1007/978-3-319-16277-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-16277-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16276-8

  • Online ISBN: 978-3-319-16277-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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