Estimates on the Size of Symbol Weight Codes

TL;DR

This paper investigates bounded and constant symbol weight codes for powerline communication, providing new bounds and constructions to improve understanding of their sizes and capabilities.

Contribution

It introduces new upper and lower bounds and offers direct and recursive constructions for bounded and constant symbol weight codes.

Findings

New upper bounds on code sizes

New lower bounds on code sizes

Explicit code constructions for specific parameters

Abstract

The study of codes for powerlines communication has garnered much interest over the past decade. Various types of codes such as permutation codes, frequency permutation arrays, and constant composition codes have been proposed over the years. In this work we study a type of code called the bounded symbol weight codes which was first introduced by Versfeld et al. in 2005, and a related family of codes that we term constant symbol weight codes. We provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes. We also give direct and recursive constructions of codes for certain parameters.