Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## On some batch code properties of the simplex code

Talk by Dr. Karan Khathuria

**Date:** 16.11.22 **Time:** 14.00 - 15.00 **Room:**

A t-batch code is a method to store a data record in an encoded form on multiple servers in such a way that the bit-values in any batch of t positions from the record can be retrieved by decoding the bit-values in t disjoint groups of positions. More generally, a t-functional batch code can be used to retrieve any batch of t linear combinations of the stored bit-values.
In 2017 by Wang et al., it was shown that the well-known binary simplex code of dimension k is a 2^(k-1)-batch code. The proof of that result is somewhat cumbersome, and the algorithm resulting from the proof requires to storing and using a database containing all the solutions for the cases where k <= 7. More recently, in 2020 Zhang et al., the authors conjecture that the k-dimensional simplex code is even a 2^(k-1)-functional batch code.
In this talk, we give a simple, algorithmic proof of a result that falls halfway between the known result for the simplex code and the conjecture. Our approach is to relate the required properties of the simplex code to certain additive problems in finite abelian groups. In addition, we formulate a new conjecture for finite abelian groups that would imply the functional batch conjectures if true for groups of the form (Z_2)^k, and we prove that this new conjecture holds for the case of cyclic groups of prime order.
This talk is based on a joint work with Henk D.L. Hollmann, Ago-Erik Riet and Vitaly Skachek.

(**This eSeminar will take place over Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact zita.fiquelideabreu@math.uzh.ch **)