New Construction of A Family of Quasi-Twisted Two-Weight Codes

TL;DR

This paper introduces a new explicit method for constructing two-weight quasi-twisted codes based on cyclic simplex codes, resulting in optimal and high-performance codes with specific parameters.

Contribution

It presents a novel construction of two-weight quasi-twisted codes from simplex codes, producing new optimal binary and ternary codes with specific parameters.

Findings

Constructed new optimal binary quasi-cyclic codes with parameters [195, 8, 96], [210, 8, 104], [240, 8, 120]

Generated good QC ternary codes with parameters [208, 6, 135], [221, 6, 144]

Many codes meet the Griesmer bound and are thus optimal.

Abstract

Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on this construction, new optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, and good QC ternary [208, 6, 135] and [221, 6, 144] codes are thus obtained. It is also shown that many codes among the family meet the Griesmer bound and thereful are optimal.