Toric surface codes and Minkowski sums

Luogo: Seminar Room “-1” – Department of Mathematics - Via Sommarive 14 - Povo -Trento
at 10:00 a.m.

• Carla Mascia - PhD in mathematics

Abstract:
Toric codes are evaluation codes obtained from an integral convex polytope P in R^n and finite field Fq. They are, in a sense, a natural extension of Reed-Solomon codes, and have been studied recently by J. Hansen and D. Joyner.
In this seminar, we show upper and lower bounds on the minimum distance of a toric code constructed from a polygon P in R^2, provided by J. Little and H. Schenck in 2005, by examining Minkowski sum decompositions of subpolygons of P.
A brief introduction to Coding Theory will be provided too.

Key words: Coding Theory, Toric Geometry, Toric codes, Minkowski sum.

Scientific Coordinators: Massimiliano Sala - Ginacarlo Rinaldo