Binary Triorthogonal and CSS-T Codes for Quantum Error Correction

TL;DR

This paper investigates binary triorthogonal codes and their connection to CSS-T quantum codes, providing characterizations of minimal and maximal codes, and methods to derive and analyze equivalent matrices for quantum error correction.

Contribution

It introduces a detailed characterization of binary triorthogonal codes and their equivalence classes, advancing the understanding of their structure and parameters in quantum error correction.

Findings

Binary triorthogonal matrices determine quantum code parameters uniquely.

Characterization of minimal and maximal triorthogonal codes within the CSS-T poset.

Methods to derive new triorthogonal matrices from existing ones.

Abstract

In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respect to the CSS-T poset, and we also study how to derive new triorthogonal matrices from existing ones. Given a binary triorthogonal matrix, we characterize which of its equivalent matrices are also triorthogonal. As a consequence, we show that a binary triorthogonal matrix uniquely determines the parameters of the corresponding triorthogonal quantum code, meaning that any other equivalent matrix that is also triorthogonal gives rise to a triorthogonal quantum code with the same parameters.