47 citations · 105 across the 18 of their papers we have counts for
20 papers
Decoding of (Interleaved) Generalized Goppa Codes
Hedongliang Liu, Sabine Pircher, Alexander Zeh +1
Generalized Goppa codes are defined by a code locator set of polynomials and a Goppa polynomial . When the degree of all code locator polynomials in $\mathcal{L…
Parity-Based Concurrent Error Detection Schemes for the ChaCha Stream Cipher
Viola Rieger, Alexander Zeh
We propose two parity-based concurrent error detection schemes for the Quarterround of the ChaCha stream cipher to protect from transient and permanent faults. They offer a trade-o…
A Public-Key Cryptosystem from Interleaved Goppa Codes
Molka Elleuch, Antonia Wachter-Zeh, Alexander Zeh
In this paper, a code-based public-key cryptosystem based on interleaved Goppa codes is presented. The scheme is based on encrypting several ciphertexts with the same Goppa code an…
Bounds and Constructions of Codes with Multiple Localities
Alexander Zeh, Eitan Yaakobi
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 loca…
Spectral Analysis of Quasi-Cyclic Product Codes
Alexander Zeh, San Ling
This paper considers a linear quasi-cyclic product code of two given quasi-cyclic codes of relatively prime lengths over finite fields. We give the spectral analysis of a quasi-cyc…
Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance
Alexander Zeh, Markus Ulmschneider
The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its generalization by Hartmann and Tzeng are lower bounds on the minimum distance of simple-root cyclic codes. We…
Optimal Linear and Cyclic Locally Repairable Codes over Small Fields
Alexander Zeh, Eitan Yaakobi
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…
Optimal Binary Locally Repairable Codes via Anticodes
Natalia Silberstein, Alexander Zeh
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 antic…
Construction of Quasi-Cyclic Product Codes
Alexander Zeh, San Ling
Linear quasi-cyclic product codes over finite fields are investigated. Given the generating set in the form of a reduced Gr{ö}bner basis of a quasi-cyclic component code and the ge…
List and Unique Error-Erasure Decoding of Interleaved Gabidulin Codes with Interpolation Techniques
Antonia Wachter-Zeh, Alexander Zeh
A new interpolation-based decoding principle for interleaved Gabidulin codes is presented. The approach consists of two steps: First, a multi-variate linearized polynomial is const…
Multi-Trial Guruswami-Sudan Decoding for Generalised Reed--Solomon Codes
Johan Sebastian Rosenkilde Nielsen, Alexander Zeh
An iterated refinement procedure for the Guruswami-Sudan list decoding algorithm for Generalised Reed-Solomon codes based on Alekhnovich's module minimisation is proposed. The meth…
Decoding of Quasi-Cyclic Codes up to A New Lower Bound on the Minimum Distance
Alexander Zeh, San Ling
A new lower bound on the minimum Hamming distance of linear quasi-cyclic codes over finite fields is proposed. It is based on spectral analysis and generalizes the Semenov- Trifono…
Multi-Trial Guruswami--Sudan Decoding for Generalised Reed--Solomon Codes
Johan Sebastian Rosenkilde Nielsen, Alexander Zeh
An iterated refinement procedure for the Guruswami--Sudan list decoding algorithm for Generalised Reed--Solomon codes based on Alekhnovich's module minimisation is proposed. The me…
Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes
Alexander Zeh, Antonia Wachter-Zeh, Maximilien Gadouleau +1
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…
A New Bound on the Minimum Distance of Cyclic Codes Using Small-Minimum-Distance Cyclic Codes
Alexander Zeh, Sergey Bezzateev
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…
Describing A Cyclic Code by Another Cyclic Code
Alexander Zeh, Sergey Bezzateev
A new approach to bound the minimum distance of -ary cyclic codes is presented. The connection to the BCH and the Hartmann--Tzeng bound is formulated and it is shown that for se…
An Interpolation Procedure for List Decoding Reed--Solomon codes Based on Generalized Key Equations
Alexander Zeh, Christian Gentner, Daniel Augot
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…
Decoding Cyclic Codes up to a New Bound on the Minimum Distance
Alexander Zeh, Antonia Wachter, Sergey Bezzateev
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 Hartm…
A Link between Guruswami--Sudan's List--Decoding and Decoding of Interleaved Reed--Solomon Codes
Alexander Zeh, Christian Senger
The Welch--Berlekamp approach for Reed--Solomon (RS) codes forms a bridge between classical syndrome--based decoding algorithms and interpolation--based list--decoding procedures f…
End-to-End Algebraic Network Coding for Wireless TCP/IP Networks
Christian Senger, Steffen Schober, Tong Mao +1
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…