### Norbert Wiener Center Archives for Academic Year 2018

#### Organizational Meeting

When: Tue, September 4, 2018 - 2:00pm

Where: Kirwan Hall 3206

Speaker: () -

#### Constrictions of bent functions using a family of permutations and Reed-Muller type codes

When: Tue, September 18, 2018 - 2:00pm

Where: Kirwan Hall 3206

Speaker: Costas Karanikas (Aristotle University of Thessaloniki) - http://users.auth.gr/karanika/

Abstract: From a pair of permutations of the first n integers we get a family of permutations on 2^n objects. This family provides new bent functions ie Boolean sequences of length 2^(2n) whose Walsh transfom get values in {2^n,- 2^n}. The left half of a bent function determines a near-bent i.e., Boolean sequences of length 2^n (n odd) with Walsh spectrum in {0,2^n,-2^n} . We relate the support of near-bents with Reed - Muller type codes and using this we construct bents of higher degree using RM type codes and bents of lower type. We also discuss several ways for constructing bent functions and modify well-known constructions as for example Dillon H class and Maiorana- McFarland method .