Applied Algebra Group at the University of Zürich 

Module: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie Event: n.n. Arbeitsgemeinschaft in Codierungstheorie und Kryptographie Linear codes with prescribed projective codewords of minimum weight
Dr. Stefan Tohaneanu 's talk Date: 31.03.21 Time: 16.00  17.00 Room: Online (**This eSeminar will take place on Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact simran.tinani@math.uzh.ch **) Consider $C$, an $[n,k,d]$linear code. Every projective codeword of minimum weight $d$ corresponds to a point in $\mathbb P^{k1}$, and there are strong connections between the algebraic and geometric properties of these points and the parameters of $C$, especially with the minimum distance $d$. The most nontrivial connection is the fact that the CastelnuovoMumford regularity of the coordinate ring of these points is a lower bound for $d$. Conversely, given a finite set of points $X$ in $\mathbb P^{k1}$, it is possible to construct linear codes with projective codewords of minimum weight corresponding to $X$. We will discuss about these constructions, and we will also look at the particular case when the constructed linear code has minimum distance equal to the regularity. 