Characterisation of the parameters of maximum weight spectrum codes according to their spread

TL;DR

This paper introduces the concept of spread in maximum weight spectrum codes, classifies sub-families based on weight distributions, and characterizes their parameters, highlighting the optimality of strictly compact MWS codes.

Contribution

It defines spread for MWS codes, classifies sub-families, and fully describes their parameters, establishing links to known codes and proving optimality.

Findings

Classified two sub-families of MWS codes based on weight distribution

Described fundamental parameters of these sub-families

Proved the optimality of strictly compact MWS codes

Abstract

We introduce the concept of spread of a code, and we specialize it to the case of maximum weight spectrum (MWS) codes. We classify two newly-defined sub-families of MWS codes according to their weight distributions, and completely describe their fundamental parameters. We focus on one of these families, the strictly compact MWS codes, proving their optimality as MWS codes and linking them to known codes.