7 citations · 12 across the 15 of their papers we have counts for
18 papers
The Asymptotic Number of Anticodes in Hamming Spaces
Anna-Lena Horlemann, Ananthakrishnan Ravi
In the Hamming space , a -anticode is a subset in which every pair of points has Hamming distance at most , or equivalently, a set of diameter at most . Le…
The Neighbor Graph of Linear Complementary Dual (LCD) Codes
Javier de la Cruz, Anna-Lena Horlemann, Marc Newman +2
Linear complementary dual (LCD) codes form an important class of linear codes with applications in cryptography, classical error correction, and quantum coding theory. In this pape…
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…
The Power of Power Codes: New Classes of Easy Instances for the Linear Equivalence Problem
Michele Battagliola, Anna-Lena Horlemann, Abhinaba Mazumder +4
Given two linear codes, the Linear Equivalence Problem (LEP) asks to find (if it exists) a linear isometry between them; as a special case, we have the Permutation Equivalence Prob…
Distinguishers for Skew and Linearized Reed-Solomon Codes
Felicitas Hörmann, Anna-Lena Horlemann
Generalized Reed-Solomon (GRS) and Gabidulin codes have been proposed for various code-based cryptosystems, though most such schemes without elaborate disguising techniques have be…
Bounds and Equivalence of Skew Polycyclic Codes over Finite Fields
Hassan Ou-azzou, Anna-Lena Horlemann, Nuh Aydin
We study skew polycyclic codes over a finite field , associated with a skew polynomial , where is an automorphism of . W…
Equivalence of Families of Polycyclic Codes over Finite Fields
Hassan Ou-azzou, Anna-Lena Horlemann
We study the equivalence of families of polycyclic codes associated with polynomials of the form over a finite field. We begin with the…
Lattice-Based Vulnerabilities in Lee Metric Post-Quantum Cryptosystems
Anna-Lena Horlemann, Karan Khathuria, Marc Newman +2
Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two…
-ary Sequential Locally Recoverable Codes from the Product Construction
Akram Baghban, Marc Newman, Anna-Lena Horlemann +1
This work focuses on sequential locally recoverable codes (SLRCs), a special family of locally repairable codes, capable of correcting multiple code symbol erasures, which are comm…
Dihedral Quantum Codes
Nadja Willenborg, Martino Borello, Anna-Lena Horlemann +1
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for…
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…
Distinguishing and Recovering Generalized Linearized Reed-Solomon Codes
Felicitas Hörmann, Hannes Bartz, Anna-Lena Horlemann
We study the distinguishability of linearized Reed-Solomon (LRS) codes by defining and analyzing analogs of the square-code and the Overbeck distinguisher for classical Reed-Solomo…
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…
Galois Hull Dimensions of Gabidulin Codes
Habibul Islam, Anna-Lena Horlemann
For a prime power , an integer and we study the -Galois hull dimension of Gabidulin codes of length and dimension over $\mat…
Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces
Anina Gruica, Anna-Lena Horlemann, Alberto Ravagnani +1
We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on…
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 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-…