Optimal additive quaternary codes of dimension $3.5$ and $4$

TL;DR

This paper determines the optimal parameters of additive quaternary codes for dimensions 3.5 and 4, and addresses the problem for arbitrary dimensions with large minimum distance.

Contribution

It completes the classification of optimal additive quaternary codes for dimensions 3.5 and 4, advancing understanding of their parameters.

Findings

Optimal parameters for dimension 3.5 codes are established.

Optimal parameters for dimension 4 codes are established.

Results apply to codes with large minimum distance for arbitrary dimensions.

Abstract

After the optimal parameters of additive quaternary codes of dimension $k\le 3$ have been determined there is some recent activity to settle the next case of dimension $k=3.5$. Here we complete dimension $k=3.5$ and $k=4$. We also solve the problem of the optimal parameters of additive quaternary codes of arbitrary dimension when assuming a sufficiently large minimum distance.