Elementary Theory of Groups and Group Rings, and Related Topics by Paul Baginski Benjamin Fine Anja Moldenhauer Gerhard Rosenberger Vladimir Shpilrain

Author:Paul Baginski, Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Vladimir Shpilrain
Language: eng
Format: epub
Publisher: De Gruyter
Published: 2020-02-10T11:45:55.611000+00:00

Definition 7.

Let G be a finite abelian multiplicative group of order v, and let D be a subset of G with order k. We say D is a -difference set (DS) if the list of differences , for , represents every nonidentity element in G exactly λ times.

A Hadamard difference set is one whose parameters are of the form or , for some . It is, in addition, elementary if G is an elementary abelian 2-group (i. e., isomorphic to , for some n).

Theorem 8 (Dillon correspondence, [11], Theorem 6.2.10, p. 78).

The function with is bent if and only if is an elementary Hadamard difference set of .

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