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|Title:||Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes||Authors:||Jin, Lingfei
|Issue Date:||2011||Source:||Jin, L., & Xing, C. (2012). Euclidean and Hermitian Self-Orthogonal Algebraic Geometry Codes and Their Application to Quantum Codes. IEEE Transactions on Information Theory, 58(8), 5484-5489.||Series/Report no.:||IEEE transactions on information theory||Abstract:||In the present paper, we show that if the dimension of an arbitrary algebraic geometry code over a finite field of even characteristic is slightly less than n/2-g with n being the length of the code and g being the genus of the base curve, then it is equivalent to an Euclidean self-orthogonal code. Previously, such results required a strong condition on the existence of a certain differential. We also show a similar result on Hermitian self-orthogonal algebraic geometry codes. As a consequence, we can apply our result to quantum codes and obtain some good quantum codes. In particular, we obtain a q-ary quantum [[q+1,1]]-MDS code for an even power q which is essential for quantum secret sharing.||URI:||https://hdl.handle.net/10356/95846
|DOI:||10.1109/TIT.2011.2177066||Rights:||© 2011 IEEE.||Fulltext Permission:||none||Fulltext Availability:||No Fulltext|
|Appears in Collections:||SPMS Journal Articles|
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