Construction of quantum codes based on self-dual orientable embeddings of complete multipartite graphs complete multipartite graphs

TL;DR

This paper introduces four new classes of binary quantum codes with minimum distances of 3 and 4, constructed using self-dual orientable embeddings of complete graphs and current graphs.

Contribution

It presents novel quantum codes derived from topological graph embeddings, expanding the methods for quantum code construction.

Findings

Four new classes of quantum codes with minimum distances 3 and 4

Codes are based on self-dual orientable embeddings of complete graphs

Construction methods involve current graphs and rotation schemes

Abstract

This paper presents four new classes of binary quantum codes with minimum dis- tance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the com- plete graphs K4r+1 and K4s and by current graphs and rotation schemes. and s are both divisible by 4.