Related Experiment Video
Updated: Oct 30, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Some New Quantum BCH Codes over Finite Fields
1The State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071, China .
Abstract:
Quantum error correcting codes (QECCs) play an important role in preventing quantum information decoherence. Good quantum stabilizer codes were constructed by classical error correcting codes. In this paper, Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields are used to construct quantum codes. First, we try to find such classical BCH codes, which contain their dual codes, by studying the suitable cyclotomic cosets. Then, we construct nonbinary quantum BCH codes with given parameter sets. Finally, a new family of quantum BCH codes can be realized by Steane's enlargement of nonbinary Calderbank-Shor-Steane (CSS) construction and Hermitian construction. We have proven that the cyclotomic cosets are good tools to study quantum BCH codes. The defining sets contain the highest numbers of consecutive integers. Compared with the results in the references, the new quantum BCH codes have better code parameters without restrictions and better lower bounds on minimum distances. What is more, the new quantum codes can be constructed over any finite fields, which enlarges the range of quantum BCH codes.
Related Concept Videos
Quantum Numbers
Fundamental Theorem of Algebra
Partial Fractions
Bulk Modulus
Quadratic Equations in the Complex Number System
Real Zeros of Polynomials

