Applied Algebra Group at the University of Zürich
Module: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie
Event: n.n. Arbeitsgemeinschaft in Codierungstheorie und Kryptographie
Batch codes from evaluation codes
Prof. Dr. Felice Manganiello's talk
Date: 13.03.19 Time: 13.30 - 14.30 Room: Uni SG 01-103
Batch codes, introduced by Ishai et al., encode a string into an m-tuple of strings, called buckets. In this talk we consider multiset batch codes wherein a set of t-users wish to access one bit of information each from the original string. We introduce a concept of optimal batch codes. The main body of this work provides batch properties of Reed-Muller codes and affine cartesian codes. We look at locality and availability properties of Reed-Muller codes over any finite field. We then show that binary first order Reed-Muller codes are optimal batch codes when the number of users is 4. We then move to another batch code construction from Reed-Muller and affine cartesian codes where buckets are elements of a quotient space of the set of points defining the codes. These results have been investigated during the 2017 and 2018 REUs at Clemson University supported by the NFS grant no. DMS:1547399.