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- Alexander Zeh, Christian Gentner, Daniel Augot
- IEEE Transactions on Information Theory
- 2011

The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding beyond half the minimum distance, are based on interpolation and factorization of multivariate polynomials. This article provides a link between syndrome-based decoding approaches… (More)

- Alexander Zeh, Eitan Yaakobi
- 2016 IEEE International Symposium on Information…
- 2016

This paper studies bounds and constructions of locally repairable codes (LRCs) with multiple localities so-called multiple-locality LRCs (ML-LRCs). In the simplest case of two localities some code symbols of an ML-LRC have a certain locality while the remaining code symbols have another one. We extend two bounds, the Singleton and the alphabet-dependent… (More)

- Alexander Zeh, Antonia Wachter-Zeh, Sergey Bezzateev
- IEEE Transactions on Information Theory
- 2012

A new lower bound on the minimum distance of <i>q</i>-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem bound and, for some codes, upon the Hartmann-Tzeng 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)

- Alexander Zeh, Eitan Yaakobi
- 2015 IEEE Information Theory Workshop (ITW)
- 2015

We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields with locality properties are developed. The first two approaches give binary cyclic codes with locality two. While the… (More)

- Natalia Silberstein, Alexander Zeh
- 2015 IEEE International Symposium on Information…
- 2015

This paper presents a construction for several families of optimal binary locally repairable codes (LRCs) with small locality (2 and 3). This construction is based on various anticodes. It provides binary LRCs which attain the Cadambe-Mazumdar bound. Moreover, most of these codes are optimal with respect to the Griesmer bound.

- Alexander Zeh, Antonia Wachter-Zeh
- Adv. in Math. of Comm.
- 2011

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)

- Christian Senger, Steffen Schober, Tong Mao, Alexander Zeh
- ArXiv
- 2009

—The Transmission Control Protocol (TCP) was designed to provide reliable transport services in wired networks. In such networks, packet losses mainly occur due to congestion. Hence, TCP was designed to apply congestion avoidance techniques to cope with packet losses. Nowadays, TCP is also utilized in wireless networks where, besides congestion, numerous… (More)

- Alexander Zeh, Sergey Bezzateev
- Des. Codes Cryptography
- 2014

A new bound on the minimum distance of q-ary cyclic codes is proposed. It is based on the description by another cyclic code with small minimum distance. The connection to the BCH bound and the Hartmann–Tzeng (HT) bound is formulated explicitly. We show that for many cases our approach improves the HT bound. Furthermore, we refine our bound for several… (More)

- Daniel Augot, Alexander Zeh
- 2008 IEEE International Symposium on Information…
- 2008

In 2000 Roth and Ruckenstein proposed an extended key equation for solving the interpolation step in the Sudan decoding algorithm. Generalizing their idea, a sequence of key equations for the Guruswami-Sudan (GS) algorithm, which is able to list decode a Reed-Solomon code with arbitrary rate, is derived. This extension allows a reduction of the number of… (More)

- Alexander Zeh, Antonia Wachter-Zeh, Maximilien Gadouleau, Sergey Bezzateev
- 2013 IEEE International Symposium on Information…
- 2013

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)