# The Complete Hierarchical Locality of the Punctured Simplex Code

## TL;DR

This paper introduces a new bound for codes with hierarchical locality, derives all possible localities for a class of punctured Simplex codes, and demonstrates their optimality in hierarchical locality.

## Contribution

It provides the first alphabet-dependent bound for hierarchical locality and characterizes the localities of punctured Simplex codes, proving their optimality.

## Key findings

- New alphabet-dependent bound for hierarchical locality
- Complete list of localities for punctured Simplex codes
- Punctured Simplex codes are optimal with hierarchical locality

## Abstract

This paper presents a new alphabet-dependent bound for codes with hierarchical locality. Then, the complete list of possible localities is derived for a class of codes obtained by deleting specific columns from a Simplex code. This list is used to show that these codes are optimal codes with hierarchical locality.