40 citations · 115 across the 12 of their papers we have counts for
15 papers
A New Path to Code-based Signatures via Identification Schemes with Restricted Errors
Marco Baldi, Massimo Battaglioni, Franco Chiaraluce +4
In this paper we introduce a variant of the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries of the searched vector are defined over a sub…
Constructing Partial MDS Codes from Reducible Curves
Tristram Bogart, Anna-Lena Horlemann-Trautmann, David Karpuk +2
We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and im…
Equivalence and Characterizations of Linear Rank-Metric Codes Based on Invariants
Alessandro Neri, Sven Puchinger, Anna-Lena Horlemann-Trautmann
We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an i…
Invariants and Inequivalence of Linear Rank-Metric Codes
Alessandro Neri, Sven Puchinger, Anna-Lena Horlemann-Trautmann
We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an i…
Information Set Decoding in the Lee Metric with Applications to Cryptography
Anna-Lena Horlemann-Trautmann, Violetta Weger
We convert Stern's information set decoding (ISD) algorithm to the ring equipped with the Lee metric. Moreover, we set up the general framework for a McEl…
Random Construction of Partial MDS Codes
Alessandro Neri, Anna-Lena Horlemann-Trautmann
This work deals with partial MDS (PMDS) codes, a special class of locally repairable codes, used for distributed storage system. We first show that a known construction of these co…
t-Private Information Retrieval Schemes Using Transitive Codes
Ragnar Freij-Hollanti, Oliver W. Gnilke, Camilla Hollanti +3
This paper presents private information retrieval (PIR) schemes for coded storage with colluding servers, which are not restricted to maximum distance separable (MDS) codes. PIR sc…
Symbol Erasure Correction Capability of Spread Codes
Heide Gluesing-Luerssen, Anna-Lena Horlemann-Trautmann
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We…
A Complete Classification of Partial-MDS (Maximally Recoverable) Codes with One Global Parity
Anna-Lena Horlemann-Trautmann, Alessandro Neri
Partial-MDS (PMDS) codes are a family of locally repairable codes, mainly used for distributed storage. They are defined to be able to correct any pattern of additional erasure…
On the Genericity of Maximum Rank Distance and Gabidulin Codes
Alessandro Neri, Anna-Lena Horlemann-Trautmann, Tovohery Randrianarisoa +1
We consider linear rank-metric codes in . We show that the properties of being MRD (maximum rank distance) and non-Gabidulin are generic over the algebraic closu…
Extension of Overbeck's Attack for Gabidulin Based Cryptosystems
Anna-Lena Horlemann-Trautmann, Kyle Marshall, Joachim Rosenthal
We present a new attack against cryptosystems based on the rank metric. Our attack allows us to cryptanalyze two variants of the GPT cryptosystem which were designed to resist the…
New Criteria for MRD and Gabidulin Codes and some Rank-Metric Code Constructions
Anna-Lena Horlemann-Trautmann, Kyle Marshall
In this work we present a new criterion to check if a given rank-metric code is a maximum rank distance (MRD) code. Moreover, we derive a criterion to check if a given MRD code is…
Message Encoding and Retrieval for Spread and Cyclic Orbit Codes
Anna-Lena Horlemann-Trautmann
Spread codes and cyclic orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability, transmissio…
Decoding of Subspace Codes, a Problem of Schubert Calculus over Finite Fields
Joachim Rosenthal, Anna-Lena Trautmann
Schubert calculus provides algebraic tools to solve enumerative problems. There have been several applied problems in systems theory, linear algebra and physics which were studied…
Spread Decoding in Extension Fields
Felice Manganiello, Anna-Lena Trautmann
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways…