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

00925njm 22002777a 4500 dc Camps Moreno, Eduardo author López, Hiram H. author Matthews, Gretchen author Ruano Benito, Diego author San José Rubio, Rodrigo author Soprunov, Ivan author 2024 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. 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 An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance