# Cliques in projective space and construction of Cyclic Grassmannian Codes

## TL;DR

This paper presents a method for constructing cyclic Grassmannian codes by identifying cliques in projective space using computational algebra systems, enhancing code design in mathematical and communication applications.

## Contribution

It introduces a novel computational approach to construct cyclic Grassmannian codes via clique detection in projective spaces.

## Key findings

- Successful construction of cliques in Pq(n)
- Generation of new cyclic Grassmannian codes
- Demonstration of computational methods for code construction

## Abstract

The construction of Grassmannian codes in some projective space is of highly mathematical nature and requires strong computational power for the resulting searches. In this paper was constructed, using GAP System for Computational Discrete Algebra and Wolfram Mathematica, cliques in the projective space Pq(n) and then we use these to produce cyclic Grassmannian codes.