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oai:uvadoc.uva.es:10324/751982025-03-03T20:01:33Zcom_10324_32197com_10324_952com_10324_894col_10324_32199

Camps Moreno, Eduardo López, Hiram H. Matthews, Gretchen Ruano Benito, Diego San José Rubio, Rodrigo Soprunov, Ivan 2025-03-03T10:15:33Z 2025-03-03T10:15:33Z 2024 Quantum Information Processing, 2024, vol. 23, n.7 https://uvadoc.uva.es/handle/10324/75198 10.1007/s11128-024-04427-5 6 Quantum Information Processing 23 1573-1332 CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes (C1, C2) such that C1 contains C2 , C2 is even, and the shortening of the dual of C1 with respect to the support of each codeword of C2 is self-dual. In this paper, we give new conditions to guarantee that a pair of binary codes (C1, C2) is a CSS-T pair. We define the poset of CSS-T pairs and determine the minimal and maximal elements of the poset. We provide a propagation rule for nondegenerate CSS-T codes. We apply some main results to Reed–Muller, cyclic and extended cyclic codes. We characterize CSS-T pairs of cyclic codes in terms of the defining cyclotomic cosets. We find cyclic and extended cyclic codes to obtain quantum codes with better parameters than those in the literature. eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ © 2024 The Author(s) Atribución 4.0 Internacional An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance info:eu-repo/semantics/article