A general family of Plotkin-optimal two-weight codes over $\mathbb{Z}_4$

TL;DR

This paper characterizes all parameters and weight distributions of Plotkin-optimal two-Lee weight projective codes over , constructs an infinite family of such codes, and relates their Gray images to two-weight binary projective codes.

Contribution

It provides a complete classification and construction of Plotkin-optimal two-Lee weight codes over , extending previous results and linking to binary codes.

Findings

All possible parameters and weight distributions are obtained.

An infinite family of two-weight codes is constructed.

Gray images match two-weight binary projective codes.

Abstract

We obtain all possible parameters of Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4,$ together with their weight distributions. We show the existence of codes with these parameters as well as their weight distributions by constructing an infinite family of two-weight codes. Previously known codes constructed by Shi et al. (\emph{Des Codes Cryptogr.} {\bf 88}(3):1-13, 2020) can be derived as a special case of our results. We also prove that the Gray image of any Plotkin-optimal two-Lee weight projective codes over $\mathbb{Z}_4$ has the same parameters and weight distribution as some two-weight binary projective codes of type SU1 in the sense of Calderbank and Kantor (\emph{Bull. Lond. Math. Soc.} {\bf 18}:97-122, 1986).