Sven Puchinger

Fast Operations on Linearized Polynomials and their Applications in Coding Theory

This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial degree

Sub-quadratic decoding of Gabidulin codes

s

Low-Area Reed Decoding in a Generalized Concatenated Code Construction for PUFs

, independent of the underlying field extension degree~

An alternative decoding method for Gabidulin codes in characteristic zero

m

Low-Rank Matrix Recovery using Gabidulin Codes in Characteristic Zero

. We show that our multiplication algorithm is faster than all known ones when

Space-time codes based on rank-metric codes and their decoding.

s \leq m

Code-Based Cryptosystems Using Generalized Concatenated Codes

. Using a result by Caruso and Le Borgne (2017), this immediately implies a sub-quadratic division algorithm for linearized polynomials for arbitrary polynomial degree

Decoding of interleaved Reed-Solomon codes using improved power decoding

s

Twisted reed-solomon codes

. Also, we propose algorithms with sub-quadratic complexity for the

Multi-block interleaved codes for local and global read access

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