24 citations · 46 across the 25 of their papers we have counts for
18 papers · 1 filter
A Survey on Code Equivalence: The State-of-the-Art and Open Questions
Anna-Lena Horlemann, Abhinaba Mazumder, Michael Schaller +1
In this work, we provide a comprehensive survey of the code equivalence problem and its variants. We explain the existing results, highlighting the relationships between different…
On Optimal Homogeneous-Metric Codes
Andreas Pyka, Violetta Weger
The homogeneous metric can be viewed as a natural extension of the Hamming metric to finite chain rings. It distinguishes between three types of elements: zero, non-zero elements i…
Weighted-Hamming Metric: Bounds and Codes
Sebastian Bitzer, Alberto Ravagnani, Violetta Weger
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independe…
Weak Composition Lattices and Ring-Linear Anticodes
Jessica Bariffi, Drisana Bhatia, Giuseppe Cotardo +1
Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties…
Weighted-Hamming Metric for Parallel Channels
Sebastian Bitzer, Alberto Ravagnani, Violetta Weger
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enabl…
Better bounds on the minimal Lee distance
Jessica Bariffi, Violetta Weger
This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the bounds using various novel definitions of generalized Lee…
On the Number of -Lee-Error-Correcting Codes
Nadja Willenborg, Anna-Lena Horlemann, Violetta Weger
We consider -Lee-error-correcting codes of length over the residue ring and determine upper and lower bounds on the number of -Le…
On the Density of Codes over Finite Chain Rings
Anna-Lena Horlemann, Violetta Weger, Nadja Willenborg
We determine the asymptotic proportion of free modules over finite chain rings with good distance properties and treat the asymptotics in the code length n and the residue field si…
The Subfield Metric and its Application to Quantum Error Correction
Markus Grassl, Anna-Lena Horlemann, Violetta Weger
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and t…
Interleaved Prange: A New Generic Decoder for Interleaved Codes
Anmoal Porwal, Lukas Holzbaur, Hedongliang Liu +3
Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosyste…
Information Set Decoding for Lee-Metric Codes using Restricted Balls
Jessica Bariffi, Karan Khathuria, Violetta Weger
The Lee metric syndrome decoding problem is an NP-hard problem and several generic decoders have been proposed. The observation that such decoders come with a larger cost than thei…
Generic Decoding in the Cover Metric
Sebastian Bitzer, Julian Renner, Antonia Wachter-Zeh +1
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as…
Bounds in the Lee Metric and Optimal Codes
Eimear Byrne, Violetta Weger
In this paper we investigate known Singleton-like bounds in the Lee metric and characterize optimal codes, which turn out to be very few. We then focus on Plotkin-like bounds in th…
Density of Free Modules over Finite Chain Rings
Eimear Byrne, Anna-Lena Horlemann, Karan Khathuria +1
In this paper we focus on modules over a finite chain ring of size . We compute the density of free modules of , where we separately treat the asy…
On Bounds for Ring-Based Coding Theory
Niklas Gassner, Marcus Greferath, Joachim Rosenthal +1
Coding Theory where the alphabet is identified with the elements of a ring or a module has become an important research topic over the last 30 years. Such codes over rings had impo…
On single server private information retrieval in a coding theory perspective
Gianira N. Alfarano, Karan Khathuria, Violetta Weger
In this paper, we present a new perspective of single server private information retrieval (PIR) schemes by using the notion of linear error-correcting codes. Many of the known sin…
On the Hardness of the Lee Syndrome Decoding Problem
Violetta Weger, Karan Khathuria, Anna-Lena Horlemann +3
In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric. We first prove that the decisional version of the problem is NP-…
Generalization of the Ball-Collision Algorithm
Carmelo Interlando, Karan Khathuria, Nicole Rohrer +2
In this paper we generalize the Ball-Collision Algorithm by Bernstein, Lange, Peters from the binary field to a general finite field. We also provide a complexity analysis and comp…