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Title: Euclidean and Hermitian self-orthogonal algebraic geometry codes and their application to quantum codes
Authors: Jin, Lingfei
Xing, Chaoping
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.
DOI: 10.1109/TIT.2011.2177066
Rights: © 2011 IEEE.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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