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We prove that Alekhnovich's algorithm can be used for row reduction of skew polynomial matrices. This yields an O(ℓ 3 n (ω+1)/2 log(n)) decoding algorithm for ℓ-Interleaved Gabidulin codes of length n, where ω is the matrix multiplication exponent, improving in the exponent of n compared to previous results.

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Abstract-Gabidulin codes, originally defined over finite fields, are an important class of rank metric codes with various applications. Recently, their definition was generalized to certain fields of characteristic zero and a Welch-Berlekamp like algorithm with complexity O(n 3 ) was given. We propose a new application of Gabidulin codes over infinite fields: low-rank matrix recovery. Also, an alternative decoding approach is presented based on a Gao type key equation, reducing the complexity to at least O(n 2 ). This method immediately connects the decoding problem to well-studied problems, which have been investigated in terms of coefficient growth and numerical stability.

Physical Unclonable Functions (PUFs) offer the possibility for on-chip generation of unique fingerprints for integrated circuits. Ring-oscillator (RO) PUFs are small and easy to configure on Field Programmable Gate Arrays (FPGAs) and thus received great attention over the years. In the state-of-the-art two neighboring ROs are compared and mapped to only a single bit of information. Few publications aims to extract more bits out of one PUF-cell, but struggle with non-uniform distributions. In this work multi-valued symbol extraction is presented as a method to extract more bits of information out of each individual RO. A new post-processing approach is introduced to produce close-to-ideal uniformly distributed responses independent of the underlying physically probability distribution. To eliminate bias, caused by placement inequalities, multiple methods of normalization are utilized and analyzed by means of area and complexity. Based on metrics for symbol transmission, the Euclidean-distance and entropy are used as metrics to evaluate the uniqueness and reliability of multi-valued PUFs. This new approach allows to increase the amount of extracted information to 3 bits per RO.