Some Results on Difference Balanced Functions

Pott, Alexander; Wang, Qi

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

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…Remark 1. In the literature (see [32]), balanced and difference-balanced functions are defined over F * q m . However, the following is clear.…”

Section: Differencementioning

confidence: 99%

“…one get a difference-balanced function over F q m ; for a difference-balanced function f on F q , the restriction of f on F * q m is a difference-balanced function over F * q m . Pott-Wang [32] tells us that a difference-balanced function f such that f (0) = 0 is always balanced. Moreover, the following is the list of all known difference-balanced functions from F q m to F q satisfying f (0) = 0:…”

Section: Differencementioning

confidence: 99%

See 1 more Smart Citation

Construction of three classes of Strictly Optimal Frequency-Hopping Sequence Sets

Ouyang¹,

Xie²,

Hu³

et al. 2019

Preprint

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“…Remark 1. In the literature (see [32]), balanced and difference-balanced functions are defined over F * q m . However, the following is clear.…”

Section: Differencementioning

confidence: 99%

Section: Differencementioning

confidence: 99%

Construction of three classes of Strictly Optimal Frequency-Hopping Sequence Sets

Ouyang¹,

Xie²,

Hu³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

Difference balanced functions and their generalized difference sets

Pott

Wang

2015

Journal of Combinatorial Theory, Series A

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Difference balanced functions from F * q n to F q are closely related to combinatorial designs and naturally define p-ary sequences with the ideal two-level autocorrelation. In the literature, all existing such functions are associated with the d-homogeneous property, and it was conjectured by Gong and Song that difference balanced functions must be d-homogeneous. First we characterize difference balanced functions by generalized difference sets with respect to two exceptional subgroups. We then derive several necessary and sufficient conditions for d-homogeneous difference balanced functions. In particular, we reveal an unexpected equivalence between the d-homogeneous property and multipliers of generalized difference sets. By determining these multipliers, we prove the Gong-Song conjecture for q prime. Furthermore, we show that every difference balanced function must be balanced or an affine shift of a balanced function.

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