Propagation Rules of Subsystem Codes

TL;DR

This paper introduces propagation rules for subsystem codes, enabling the construction of new codes with varied parameters through extension, shortening, and combination methods.

Contribution

It provides a systematic way to generate new subsystem codes from existing ones by applying specific propagation rules.

Findings

New subsystem codes with varied parameters derived from existing codes.

Extension and shortening methods preserve or improve code distance.

Framework for constructing diverse subsystem codes.

Abstract

We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an $[[n,k,r,d]]_q$ subsystem code, we drive new subsystem codes with parameters $[[n+1,k,r,\geq d]]_q$, $[[n-1,k+1,r,\geq d-1]]_q$, $[[n,k-1,r+1,d]]_q$. The interested readers shall consult our companion papers for upper and lower bounds on subsystem codes parameters, and introduction, trading dimensions, families, and references on subsystem codes [1][2][3] and references therein.