Geodesic
Quasi-cyclic alternant codes and analysis of their security in cryptographic applications
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 147-152

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The paper presents an overview of quasi-cyclic alternant codes and their structural analysis regarding the classification of automorphisms. Also, we describe in detail methods for restoring the structure of a given code. The attractiveness of the family of considered codes lies in its cryptographic applications, and, as in theory, in reducing the key length of post-quantum code-based schemes. In addition, this method of constructing codes is universal and can be used to obtain alternant codes of quasi-cyclic algebraic-geometric codes associated with an arbitrary curve with a known group of automorphisms. However, as shown in the work, as a result of constructing quasi-cyclic alternant codes, it becomes possible to reduce the key security of the source code to a code with smaller parameters, which may not be resistant to a structural attack.
Mots-clés : quasi-cyclic codes, alternant codes, invariant codes, automorphism group of a code.
Keywords: algebraic-geometric code, function fields 
@article{PDMA_2024_17_a37,
     author = {A. A. Kuninets},
     title = {Quasi-cyclic alternant codes and analysis of their security in cryptographic applications},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {147--152},
     publisher = {mathdoc},
     number = {17},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2024_17_a37/}
}
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A. A. Kuninets. Quasi-cyclic alternant codes and analysis of their security in cryptographic applications. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 147-152. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a37/