Duality and Decoding of Linearized Algebraic Geometry Codes

Polynomial decoding algorithm for Algebraic Geometry (AG) codes have been known since the 90's. In 2023, Xavier Caruso and Elena Berardini introduced a generalization of AG codes called Linearized Algebraic Geometry (LAG) codes, a family of sum-rank metric evaluation codes on division algebras over function fields.

Until our very recent joint work "Duality and decoding of linearized Algebraic Geometry codes" with the same authors no polynomial decoding algorithm was known for these LAG codes. In this presentation, we will show how we designed and proved our decoding algorithm, developing to this end a novel Riemann--Roch theory on division algebras.