New quaternary codes derived from posets of the disjoint union of two chains

TL;DR

This paper introduces a new method for constructing linear codes over Z_4 using posets of disjoint unions of chains, determining their weight distributions and deriving new quaternary and binary codes.

Contribution

It presents a novel construction of linear Z_4-codes based on posets of disjoint chains, expanding the class of known codes with specific weight distributions.

Findings

Determined Lee weight distributions of the constructed codes.

Obtained new linear quaternary codes.

Derived good binary codes via Gray map.

Abstract

Based on the generic construction of linear codes, we construct linear codes over the ring $\Bbb Z_4$ via posets of the disjoint union of two chains. We determine the Lee weight distributions of the quaternary codes. Moreover, we obtain some new linear quaternary codes and good binary codes by using the Gray map.