Decoding of Interleaved Reed-Solomon Codes Using Improved Power Decoding

We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code length $n$. For $m>2$, this is an asymptotic improvement over the previous state-of-the-art for all rates, and the first improvement for $R>1/3$ in the last $20$ years. The method combines collaborative decoding of IRS codes with power decoding up to the Johnson radius.Comment: 5 pages, accepted at IEEE International Symposium on Information Theory 201

Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography

We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.Comment: 5 pages, accepted at: IEEE International Symposium on Information Theory 201

Further Generalisations of Twisted Gabidulin Codes

We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes.Comment: 10 pages, accepted at the International Workshop on Coding and Cryptography (WCC) 201