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Full-Text Articles in Physical Sciences and Mathematics
Algebraic Techniques In Designing Quantum Synchronizable Codes, Yuichiro Fujiwara, Vladimir Tonchev, Tony Wong
Algebraic Techniques In Designing Quantum Synchronizable Codes, Yuichiro Fujiwara, Vladimir Tonchev, Tony Wong
Department of Mathematical Sciences Publications
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable magnitude of block synchronization errors while giving mathematical insight into the algebraic mechanism of synchronization recovery. Also given are families of quantum synchronizable codes based on punctured Reed-Muller codes and their ambient spaces.
Enumeration Of (16,4,16,4) Relative Difference Sets, David C. Clark, Vladimir Tonchev
Enumeration Of (16,4,16,4) Relative Difference Sets, David C. Clark, Vladimir Tonchev
Department of Mathematical Sciences Publications
A complete enumeration of relative difference sets (RDS) with parameters (16, 4, 16, 4) in a group of order 64 with a normal subgroup N of order 4 is given. If N = Z4 , three of the 11 abelian groups of order 64, and 23 of the 256 nonabelian groups of order 64 contain (16, 4, 16, 4) RDSs. If N = Z2 × Z2 , nine of the abelian groups and 194 of the non-abelian groups of order 64 contain (16, 4, 16, 4) RDSs.