eSeminar: Asymptotic performance of G-codes and uncertainty principle.

Vortrag von Dr. Martino Borello

Datum: 16.12.20  Zeit: 15.00 - 16.00  Raum:

<a href="https://uzh.mediaspace.cast.switch.ch/media/Martino%20Borello%3A%20Asymptotic%20performance%20of%20G-codes%20and%20uncertainty%20principle./0_t8jtm53u/11634" target="_blank"><button>Video<i class="fa fa-play-circle"></i></button></a> <a href="https://www.math.uzh.ch/aa/uploads/media/borello_gcodes.pdf" target="_blank"><button>Slides<i class="fa fa-play-circle"></i></button></a><br><br> (**This eSeminar will take place on Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact karan.khathuria@math.uzh.ch **) <BR> <BR> The uncertainty principle is a very famous inequality in Physics, Signal Processing, and Harmonic Analysis. It compares the supports of functions and of their complex-valued Fourier transforms. In a recent paper by Evra, Kowalski, and Lubotzky a connection between the uncertainty principle and the asymptotic performance of cyclic codes was pointed out. Note that the existence of an asymptotically good family of cyclic codes is a problem open for more than half a century. In the first part of the talk, we will present some recent results about the asymptotic performance of group codes, which are a generalization of cyclic codes. In the second part, we will give an overview of conjectural and proved results about the uncertainty principle over finite fields. A naive version of this principle, which is verified by any finite field, implies that there exist sequences of cyclic codes of length n, arbitrary rate, and minimum distance Ω(n^α) for all 0 < α < 1/2.