A Combinatorial Interpretation for the Shor-Laflamme Weight Enumerators of CWS Codes

TL;DR

This paper reveals that a specific quantum code weight enumerator can be understood as a classical code's distance enumerator, bridging quantum and classical coding theory insights.

Contribution

It provides a novel combinatorial interpretation linking quantum code weight enumerators to classical code distance enumerators.

Findings

Establishes a direct correspondence between quantum and classical code enumerators.

Offers a new perspective for analyzing quantum codes using classical coding theory.

Enhances understanding of the structure of codeword stabilized quantum codes.

Abstract

We show that one of the Shor-Laflamme weight enumerators of a codeword stabilized quantum code may be interpreted as the distance enumerator of an associated classical code.