2008/03/07 by Valentin Savin, Savin, Valentin
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.0803.1096
openalex publication_date 2008/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Algebraic-geometric codes can be constructed by evaluating a certain set of functions on a set of distinct rational points of an algebraic curve. The set of functions that are evaluated is the linear space of a given divisor or, equivalently, the set of section of a given line bundle. Using arbitrary rank vector bundles on algebraic curves, we propose a natural generalization of the above construction. Our codes can also be seen as interleaved versions of classical algebraic-geometric codes. We show that the algorithm of Brown, Minder and Shokrollahi can be extended to this new class of codes and it corrects any number of errors up to t* - g/2, where t* is the designed correction capacity of the code and g is the curve genus.