Weight distributions, zeta functions and Riemann hypothesis for linear and algebraic geometry codes

TL;DR

This survey explores the connections between weight distributions, zeta functions, and the Riemann hypothesis in the context of linear and algebraic-geometry codes, highlighting theoretical insights and open problems.

Contribution

It provides a comprehensive overview of the current state of research on weight enumerators and zeta functions in coding theory, emphasizing the Riemann hypothesis aspect.

Findings

Summarizes key results on weight enumerators and zeta functions.

Discusses the status of the Riemann hypothesis for these codes.

Identifies open problems and future research directions.

Abstract

This is a survey on weight enumerators, zeta functions and Riemann hypothesis for linear and algebraic-geometry codes.