Perfect sequences, arrays, and quaternions

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
Ore: 11:00

Relatore:

•  Heiko Dietrich  ( Monash University Melbourne)

Abstract:

The periodic autocorrelation of a sequence is a measure for how much the sequence differs from its cyclic shifts. If the autocorrelation values for all nontrivial cyclic shifts are 0, then the sequence is perfect. Perfect sequences have important applications in information technology and engineering, however, it is very difficult to construct them over n-th roots of unities: in fact, it is conjectured that they do not exist for lengths greater that n^2. There has been some focus on other classes of sequences with good autocorrelation. One of these classes is the family of perfect sequences over the quaternions. We discuss some properties of new perfect sequences over quaternions, generalisations to perfect arrays, and a connection to Hadamard matrices. This is joint work with Santiago Barrera Acevedo.

Contact person:  Willem Adriaan De Graaf