caa a22 4500 475807278 CHVBK 20180406123750.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1023/A:1008323618944 doi (NATIONALLICENCE)springer-10.1023/A:1008323618944 Wolfmann Jacques G.E.C.T., Université de Toulon, 83130, La Garde, FRANCE aut Difference Sets in $${\mathbb{Z}}_4^m$$ and $${\mathbb{F}}_2^{2m}$$ [Elektronische Daten] [Jacques Wolfmann] Let R=GR(4,m) be the Galois ring of cardinality 4m and let T be the Teichmüller system of R. For every map λ of T into { -1,+1} and for every permutation Π of T, we define a map φ λ Π of Rinto { -1,+1} as follows: if x∈R and if x=a+2b is the 2-adic representation of x with x∈T and b∈T, then φ λ Π (x)=λ(a)+2Tr(Π(a)b), where Tr is the trace function of R . For i=1 or i=-1, define D i as the set of x in R such thatφ λ Π =i. We prove the following results: 1) D i is a Hadamard difference set of (R,+). 2) If φ is the Gray map of R into $${\mathbb{F}}_2^{2m}$$ , then (D i) is a difference set of $${\mathbb{F}}_2^{2m}$$ . 3) The set of D i and the set of φ(D i) obtained for all maps λ and Π, both are one-to-one image of the set of binary Maiorana-McFarland difference sets in a simple way. We also prove that special multiplicative subgroups of R are difference sets of kind D i in the additive group of R. Examples are given by means of morphisms and norm in R. Kluwer Academic Publishers, 2000 difference sets nationallicence Galois ring nationallicence Gray map nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 20/1(2000-04-01), 73-88 0925-1022 20:1<73 2000 20 10623 https://doi.org/10.1023/A:1008323618944 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008323618944 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wolfmann Jacques G.E.C.T., Université de Toulon, 83130, La Garde, FRANCE aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 20/1(2000-04-01), 73-88 0925-1022 20:1<73 2000 20 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer