7 citations · 12 across the 15 of their papers we have counts for
12 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…
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…
-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…
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-…