Title :
Stabilizer codes over Frobenius rings
Author :
Nadella, Sushma ; Klappenecker, Andreas
Author_Institution :
Dept. of Comput. Sci. & Eng., Texas A&M Univ., College Station, TX, USA
Abstract :
Quantum error-correcting codes over finite fields have been widely studied, but quantum codes over rings have been left largely unexplored. This paper introduces stabilizer codes over finite Frobenius rings and establishes their connection to classical code. Structural properties of stabilizer codes over finite Frobenius rings are established. It is proved that free stabilizer codes over finite commutative chain rings cannot outperform stabilizer codes over finite fields.
Keywords :
error correction codes; classical code; finite Frobenius rings; finite commutative chain rings; finite fields; free stabilizer codes; quantum error-correcting codes; stabilizer codes; Additives; Indexes; Jacobian matrices; Kernel; Linear code; Shape; Structural rings;
Conference_Titel :
Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
978-1-4673-2580-6
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2012.6283558
