CSS-T codes from cyclic codes

This is the repository for the codes obtained in the paper "E. Camps-Moreno, H.H. López, G.L. Matthews, D. Ruano, R. San-José, I. Soprunov. An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance. Quantum Inf Process 23, 230 (2024)". DOI: https://doi.org/10.1007/s11128-024-04427-5

Files

For a given CSS-T code with parameters [[n,k,d]], the zip archive Matrices.zip contains a parity check matrix for C1 in the files "n_k_d_C1.txt" and "n_k_d_C1.npy". Similarly for C2.

-The .txt files contain in the first line the cyclotomic sets used to construct the (extended) cyclic codes (resp. the degree for Reed-Muller codes), and the parity check matrix in plain text. For non-extended cyclic codes, we use 0 instead of n for the cyclotomic sets (with respect to the paper).

-The .npy files contain the parity check matrix in binary format. We provide below an example to load this matrix with Python and SageMath.

Example to load the matrices for the code [[32,4,4]]

Python:

import numpy

H1=numpy.load('32_4_4_C1.npy')

H2=numpy.load('32_4_4_C2.npy')

(H1 and H2 are the parity check matrices of C1 and C2 in numpy array format)

SageMath

import numpy

A1=numpy.load('32_4_4_C1.npy')

A2=numpy.load('32_4_4_C2.npy')

H1=matrix(GF(2),A1)

H2=matrix(GF(2),A2)

C1=LinearCode(H1).dual_code()

C2=LinearCode(H2).dual_code()