Binary Triorthogonal and CSS-T Codes for Quantum Error Correction
Information Theory
2024-08-07 v1 math.IT
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.
Cite
@article{arxiv.2408.02916,
title = {Binary Triorthogonal and CSS-T Codes for Quantum Error Correction},
author = {Eduardo Camps-Moreno and Hiram H. López and Gretchen L. Matthews and Diego Ruano and Rodrigo San-José and Ivan Soprunov},
journal= {arXiv preprint arXiv:2408.02916},
year = {2024}
}