Classification of binary systematic codes of small defect

TL;DR

This paper classifies non-linear binary systematic AMDS codes of small defect based on their weight distributions, showing that length and minimum distance fully determine these distributions using elementary methods.

Contribution

It provides a complete classification of certain binary systematic codes by their weight distributions, highlighting the role of length and minimum distance.

Findings

Weight distribution is determined by length and minimum distance.

Non-trivial non-linear binary systematic AMDS codes are classified.

Elementary techniques suffice for the classification.

Abstract

In this paper non-trivial non-linear binary systematic AMDS codes are classified in terms of their weight distributions, employing only elementary techniques. In particular, we show that their length and minimum distance completely determine the weight distribution.