Section: New Results
Participants : Xavier Caruso, Aurel Page.
In , Xavier Caruso developed a theory of residues for skew rational functions (which are, by definition, the quotients of two skew polynomials), proving in particular a skew analogue of the residue formula and a skew analogue of the classical formula of change of variables for residues. He then used his theory to define and study a linearized version of Goppa codes. He showed that these codes meet the Singleton bound (for the sum-rank metric) and are the duals of the linearized Reed–Solomon codes defined recently by Martínez-Peñas. Efficient encoding and decoding algorithms are also designed.
C. Maire and A. Page updated the preprint Error-correcting codes based on non-commutative algebras  according to the comments of referees.