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Séminaire de Théorie Algorithmique des Nombres

Linearised Chinese Remainder Codes

Camille Garnier

( Université de Limoges )

Salle 2

le 22 avril 2025 à 11:00

We introduce a new family of rank metric codes. The construction of these codes relies on the "Chinese Remainder Theorem" for linearised polynomials. Linearised polynomials are polynomials in which the exponents of all the monomials are powers of q and the coefficients come from an extension field of the finite field of order q. The set of these polynomials forms a right Euclidean ring. We present the lifting of the isomorphism of the Chinese remainder theorem for linearised polynomials. We show how this lifting leads to a decoding algorithm for a special case of this family of codes: the case where the linearised polynomials have coefficients in the finite field of order q. (Joint work with Olivier Ruatta and Philippe Gaborit).