Additive codes from linear codes

TL;DR

This paper presents two new methods for constructing additive codes over larger finite fields from existing linear codes, resulting in codes with proven good minimum distances.

Contribution

It introduces novel constructions of additive codes derived from linear codes, enhancing code design over finite fields.

Findings

Constructed additive codes with good minimum distances.

Provided explicit methods starting from linear codes.

Demonstrated the effectiveness of the constructions.

Abstract

We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is demonstrably good.