On the Construction for Quantum Code ((n,K, d))p via Logic Function over Fp

TL;DR

This paper presents a method to construct quantum codes using logic functions over finite fields, establishing bounds on code parameters and conditions for optimality.

Contribution

It introduces a new construction approach for quantum codes based on logic functions with APC distance, linking classical logic properties to quantum code parameters.

Findings

Established a relation between APC distance and quantum code distance.

Derived bounds on the dimension K for given code distances.

Discussed conditions for saturating the quantum Singleton bound.

Abstract

This paper studies the construction for quantum codes with parameters $((n,K,d))_{p}$ by use of an \textit{n}-variable logic function with APC distance $d'\ge 2$ over ${\rm {\mathbb F}}_{p} $, where $d$ is related to $d'$. We obtain $d\le d'$ and the maximal $K$ for all $d=d'-k$, $0\le k\le d'-2$. We also discuss the basic states and the equivalent conditions of saturating quantum Singleton bound.