EE Seminar: Subspace polynomials, cyclic subspace codes, and list-decoding of Gabidulin codes

~~(The talk will be given in English)

Speaker:  Netanel Raviv
                        Computer Science Department, Technion

Monday, April 18th, 2016
15:00 - 16:00
Room 011, Kitot Bldg., Faculty of Engineering

Subspace polynomials, cyclic subspace codes, and list-decoding of Gabidulin codes

Abstract
Subspace codes have received an increasing interest recently due to their application in error correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and decoding algorithms. We introduce a new way of representing subspace codes by a class of polynomials called subspace polynomials. We present some constructions of such codes which are cyclic and analyze their parameters.

In addition, the subspace polynomials from one of these constructions is used to show the limits of list decoding of Gabidulin codes, which may be seen as the rank-metric equivalent of Reed-Solomon codes. Our results show that unlike Reed-Solomon codes, there exists certain Gabidulin codes that cannot be list decoded efficiently beyond the unique decoding radius.

Bio: Netanel Raviv received a B.Sc. from the department of mathematics and an M.Sc. from the department of Computer Science at the Technion at 2010 and 2013, respectively. He is now a Doctoral student at the department of Computer Science at the Technion. He is an awardee of the IBM Ph.D. fellowship for the academic year of 2015-2016, and the Aharon and Ephraim Katzir study grant for 2015. His research interests include coding for distributed storage systems, algebraic coding theory, network coding, and algebraic structures.