# Vard{\o}hus Codes: Polar Codes Based on Castle Curves Kernels

## TL;DR

This paper explores the use of algebraic Castle Curves to construct kernels for polar codes, analyzing their minimum distance, duals, and matrix exponents to improve code performance.

## Contribution

It introduces a novel method of constructing polar code kernels using Castle Curves, linking algebraic geometry with coding theory.

## Key findings

- Constructed polar code kernels from Castle Curves
- Analyzed minimum distance and duals of the codes
- Studied exponents of the defining matrices

## Abstract

In this paper, we show some applications of algebraic curves to the construction of kernels of polar codes over a discrete memoryless channel which is symmetric w.r.t the field operations. We will also study the minimum distance of the polar codes proposed, their duals and the exponents of the matrices used for defining them. All the restrictions that we make to our curves will be accomplished by the so-called Castle Curves.