Lifted Codes and Lattices from Codes Over Finite Chain Rings

TL;DR

This paper generalizes lifted codes over finite chain rings using $p$-adic fields and introduces a lattice construction from these codes, expanding coding theory frameworks.

Contribution

It provides a new generalization of lifted codes over finite chain rings and proposes a novel lattice construction from these codes.

Findings

Generalization of lifted codes to all finite chain rings.

Construction of lattices from codes over finite chain rings.

Use of $p$-adic fields in code construction.

Abstract

In this paper we give the generalization of lifted codes over any finite chain ring. This has been done by using the construction of finite chain rings from $p$-adic fields. Further we propose a lattice construction from linear codes over finite chain rings using lifted codes.