Antonia Wachter-Zeh

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—A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose– Chaudhuri–Hocquenghem (BCH) bound and, for some codes, upon the Hartmann–Tzeng (HT) bound. Several Boston bounds are special cases of our bound. For some classes of codes the bound on the minimum distance is refined. Furthermore, a quadratic-time(More)
—So far, there is no polynomial-time list decoding algorithm (beyond half the minimum distance) for Gabidulin codes. These codes can be seen as the rank-metric equivalent of Reed–Solomon codes. In this paper, we provide bounds on the list size of rank-metric codes in order to understand whether polynomial-time list decoding is possible or whether it works(More)
Feng and Tzeng's generalization of the Extended Euclidean Algorithm synthesizes the shortest–length linear feedback shift–register for s ≥ 1 sequences, where each sequence has the same length n. In this contribution, it is shown that Feng and Tzeng's algorithm which solves this multi–sequence shift–register problem has time complexity O(sn 2). An(More)
—Two generalizations of the Hartmann–Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique decoding up to this bound is always possible and outline a quadratic-time syndrome-based error decoding algorithm. The second(More)
A new probabilistic decoding algorithm for low-rate Interleaved Reed– Solomon (IRS) codes is presented. This approach increases the error correcting capability of IRS codes compared to other known approaches (e.g. joint decoding) with high probability. It is a generalization of well-known decoding approaches and its complexity is quadratic with the length(More)
(Partial) Unit Memory ((P)UM) codes provide a powerful possibility to construct convolutional codes based on block codes in order to achieve a high decoding performance. In this contribution, a construction based on Gabidulin codes is considered. This construction requires a modified rank metric, the so–called sum rank metric. For the sum rank metric, the(More)
This paper considers fast algorithms for operations on linearized polynomials. Among these results are fast algorithms for division of linearized polynomials, q-transform, multi-point evaluation, computing minimal subspace polynomials and interpolation. The complexity of all these operations is now sub-quadratic in the q-degree of the linearized(More)