Generator kodow liniowych o skonczonych charakterystykach

TL;DR

This paper introduces a novel method for generating certain families of linear codes over finite fields with characteristics greater than two, utilizing embeddings of projective lines into Grassmann manifolds, especially when dimension equals codimension.

Contribution

It proposes a new approach to construct linear codes over finite fields by embedding projective lines into Grassmann manifolds, expanding the class of codes that can be generated.

Findings

Effective code generation over finite fields with characteristic > 2

Utilizes embedding of projective lines into Grassmann manifolds

Applicable when dimension equals codimension

Abstract

The paper presents a method to generate some families of linear codes over finite fields of characteristics greater than two in the widest class due to the size of Grassmann manifold, i.e. when the dimension is equal to codimension. Our method applies some simple embedding of projective line into the Grassman manifold.