Geodesic
Construction of quasi-cyclic alternant codes and~their application in code-based cryptography
Prikladnaâ diskretnaâ matematika, no. 3 (2024), pp. 84-109

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The paper presents an overview of quasi-cyclic alternant codes and their structural analysis regarding the classification of automorphisms. We also have detailed methods for recovering the structure of a given code. The attractiveness of the family of considered codes lies in their 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 subfield subcodes of quasi-cyclic algebraic-geometric codes associated with an arbitrary curve with a known group of automorphisms. However, 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 
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     author = {A. A. Kuninets and E. S. Malygina},
     title = {Construction of quasi-cyclic alternant codes and~their application in code-based cryptography},
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A. A. Kuninets; E. S. Malygina. Construction of quasi-cyclic alternant codes and~their application in code-based cryptography. Prikladnaâ diskretnaâ matematika, no. 3 (2024), pp. 84-109. http://geodesic.mathdoc.fr/item/PDM_2024_3_a4/