A recursive construction for skew Hadamard difference sets
The electronic journal of combinatorics, Tome 27 (2020) no. 3
A major conjecture on the existence of abelian skew Hadamard difference sets is: if an abelian group $G$ contains a skew Hadamard difference set, then $G$ must be elementary abelian. This conjecture remains open in general. In this paper, we give a recursive construction for skew Hadamard difference sets in abelian (not necessarily elementary abelian) groups. The new construction can be considered as a result on the aforementioned conjecture: if there exists a counterexample to the conjecture, then there exist infinitely many counterexamples to it. A corrigendum was added to this paper on June 9, 2021.
@article{10_37236_9058,
author = {Koji Momihara},
title = {A recursive construction for skew {Hadamard} difference sets},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {3},
doi = {10.37236/9058},
zbl = {1446.05011},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9058/}
}
Koji Momihara. A recursive construction for skew Hadamard difference sets. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/9058
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