21 Feb 2008; Mat-Nat Faculty (UiTø), room A228. Thursday 12:15-14:00
"Error-correcting codes from algebraic geometry".
An error-correcting code is simply a vector subspace of (Fq )^n for a finite field Fq.
For traditional Goppa codes one uses points and divisors of algebraic curves, defined over a finite field Fq, to produce such codes. In this talk we sketch the main steps in the construction of Goppa codes, and the basic properties of such codes. One can also use Fq-rational points of certain algebraic varieties of higher dimensions to produce error-correcting codes in a similar way. Examples are Grassmannians, flag varieties and rational normal scrolls.
We will describe techniques for how to determine the code parameters, including the higher support weights, of some of these codes, with special emphasis on scrollar codes.