CSS-$T$ codes over Binary Extension Fields and their Physical Foundations

Jasper J. Postema; F. Conca; A. Ravagnani

CSS-$T$ codes over Binary Extension Fields and their Physical Foundations

Quantum Physics 2025-07-24 v1

Authors: Jasper J. Postema , F. Conca , A. Ravagnani

Abstract

We investigate the class of CSS- $T$ codes, a family of quantum error-correcting codes that allows for a transversal $T$ -gate. We extend the definition of a pair of linear codes $(C_1,C_2)$ , $C_i\subseteq\mathbb{F}_q^n$ , forming a $q$ -ary CSS- $T$ code over binary extension fields, and demonstrate the existence of asymptotically good sequences of LDPC CSS- $T$ codes over any such field.

Keywords

quantum error correction

Cite

@article{arxiv.2507.17611,
  title  = {CSS-$T$ codes over Binary Extension Fields and their Physical Foundations},
  author = {Jasper J. Postema and F. Conca and A. Ravagnani},
  journal= {arXiv preprint arXiv:2507.17611},
  year   = {2025}
}