720 citations
- University of Applied Sciences St. GallenCH12 papers
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8 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…
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…
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…
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…
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…