Linearized Polynomial Chinese remainder codes

TL;DR

This paper introduces a new family of codes based on linearized polynomials and Chinese remainder theorem, suitable for rank and sum-rank metrics, with a decoding algorithm for certain cases.

Contribution

It presents a novel code construction using linearized polynomials and Chinese remainders, expanding coding options for rank-based metrics.

Findings

Codes applicable to rank and sum-rank metrics

Decoding algorithm for specific code instances

Utilizes Chinese remainders theorem for linearized polynomials

Abstract

In this paper, we introduce a new family of codes relevent for rank and sum-rank metrics. These codes are based on an effective Chinese remainders theorem for linearized polynomials over finite fields. We propose a decoding algorithm for some instances of these codes.