Year: 2026
Type: preprint
Abstract: CSS-T codes are quantum error-correcting codes that play an important role in fault-tolerant quantum computation, as they help mitigate the proliferation of errors. They admit a transversal T-gate and are defined from a pair of nested classical binary linear codes satisfying a specific algebraic condition expressed in terms of their Schur square. We extend this algebraic characterization to the propagation rule known as the $(u \mid u+v)$-construction, that is, the matrix-product code constructed from two constituent codes. Moreover, for cyclic constituent codes, we provide an explicit characterization in terms of the defining cyclotomic sets, which extends existing results for cyclic codes. This framework allows the construction of new and longer CSS-T codes.
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Istituto Nazionale di Alta Matematica "Francesco Severi", Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Junta de Castilla y León, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, European Regional Development Fund, Agencia Estatal de Investigación
OpenAlex ID: W7212047498