Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655247 | Journal of Combinatorial Theory, Series A | 2015 | 10 Pages |
Abstract
Difference balanced functions from Fqnâ to Fq 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 have the homogeneous property, and it was conjectured by Gong and Song that difference balanced functions must be d-homogeneous for some d with gcdâ¡(d,qâ1)=1. Here we characterize difference balanced functions by difference sets with respect to two exceptional subgroups. We then reveal an unexpected equivalence between the homogeneous property and certain multipliers of the corresponding difference sets. By determining these multipliers, we prove the Gong-Song conjecture for q prime.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Alexander Pott, Qi Wang,