K. T. Arasu (Wright State University, Dayton, ZDA): Perfect Sequence constructions

Povzetek: This talk will deal with some new constructions of sequences and arrays whose auto-correlation functions having desirable correlation properties. Of particular interest are the p-ary sequences, where p is a prime, and the entries of the underlying sequence are p-th roots of unity. The ternary case has entries that are complex third roots of unity . In this case, the prefix "perfect" for the underlying sequence (i.e. 1-dimensional array) refers to the case when all the out-of-phase autocorrelations are equal to minus one. In this talk, we give some new construction methods for these interesting combinatorial objects. The main tools used in our new research are: Stickelberger congruence on Gauss Sums and Hasse-Davenport formulae. This is a joint work with John Dillon and Kevin Player. The inequivalence of the new sequences follows by the p-rank calculations of the associated matrices.