Section: New Results

Coding Theory

Participants : Xavier Caruso, Aurel Page.

In [29], 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 [33] according to the comments of referees.