Residues of skew rational functions and linearized Goppa codes

08/22/2019 ∙ by Xavier Caruso, et al. ∙ 0

This paper constitutes a first attempt to do analysis with skew polynomials. Precisely, our main objective is to develop a theory of residues for skew rational functions (which are, by definition, the quotients of two skew polynomials). We prove in particular a skew analogue of the residue formula and a skew analogue of the classical formula of change of variables for residues. We then use our theory to define and study a linearized version of Goppa codes. We show 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. We also design efficient encoding and decoding algorithms for them.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.