On the classification of $\mathbb{Z}_4$-codes

TL;DR

This paper classifies certain $bZ_4$-codes of small lengths, providing explicit classifications for special cases and completing an exhaustive search for lengths up to 7.

Contribution

It offers a detailed classification of $bZ_4$-codes for specific parameters and length up to 7, advancing understanding of their structure.

Findings

Complete classification of $bZ_4$-codes of length up to 7.

Explicit classification for special cases $(k_1,k_2)$.

Identification of conditions for code classification.

Abstract

In this note, we study the classification of $\mathbb{Z}_4$-codes. For some special cases $(k_1,k_2)$, by hand, we give a classification of $\mathbb{Z}_4$-codes of length $n$ and type $4^{k_1}2^{k_2}$ satisfying a certain condition. Our exhaustive computer search completes the classification of $\mathbb{Z}_4$-codes of lengths up to $7$.