A Survey on Codes from Simplicial Complexes

TL;DR

This survey reviews recent developments in codes constructed from simplicial complexes, highlighting key results and proposing open problems to stimulate future research in this mathematical area.

Contribution

It provides a comprehensive overview of recent results and introduces open problems to guide future research in codes from simplicial complexes.

Findings

Summarizes recent advances in codes from simplicial complexes

Highlights open problems for future research

Encourages further exploration of combinatorial code structures

Abstract

In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning that every subset of a set within the family is also included in the family. The purpose of this paper is two-fold. Firstly, it aims to present a comprehensive survey of recent results in the field. This survey intends to provide an overview of the advancements made in codes constructed from simplicial complexes. Secondly, the paper seeks to propose open problems that are anticipated to stimulate further research in this area. By highlighting these open problems, the paper aims to encourage and inspire future investigations and developments in the field of codes derived from simplicial complexes.