Talk by Dr. Alessandro Neri
Speaker invited by: Prof. Dr. Joachim Rosenthal
Date: 07.12.22 Time: 16.30 - 17.30 Room: Y27H12
Minimal linear codes were first introduced by Cohen and Lempel over the binary field with the name of linear intersecting codes. They later gained interest due to their use in secret sharing schemes proposed by Massey. Recently, it has been shown that k-dimensional minimal linear codes are in one-to-one correspondence with strong blocking sets in a (k-1)-dimensional projective space. Strong blocking sets are sets of points such that their intersection with each hyperplane generates the hyperplane itself, and they were originally introduced as a tool for constructing covering codes.
In this talk we propose a new general method to construct small strong blocking sets - and hence short minimal linear codes - starting from a set of points in a finite projective space and a graph with large vertex integrity. In particular, we explore how one can get explicit constructions of families of asymptotically good minimal linear codes, combining Ramanujan graphs and families of asymptotically good linear codes.
This is a joint work with Noga Alon, Anurag Bishnoi and Shagnik Das.
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