1. An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance.
- Author
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Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, San-José, Rodrigo, and Soprunov, Ivan
- Subjects
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CYCLIC codes , *BINARY codes , *FAULT tolerance (Engineering) , *ERROR-correcting codes , *LINEAR codes , *FAULT-tolerant computing - Abstract
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 (C 1 , C 2) such that C 1 contains C 2 , C 2 is even, and the shortening of the dual of C 1 with respect to the support of each codeword of C 2 is self-dual. In this paper, we give new conditions to guarantee that a pair of binary codes (C 1 , C 2) 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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