Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/95846
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.
URI: https://hdl.handle.net/10356/95846
http://hdl.handle.net/10220/11432
DOI: 10.1109/TIT.2011.2177066
Rights: © 2011 IEEE.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

SCOPUSTM   
Citations

27
checked on Sep 1, 2020

WEB OF SCIENCETM
Citations

25
checked on Oct 27, 2020

Page view(s)

335
checked on Oct 26, 2020

Google ScholarTM

Check

Altmetric


Plumx

Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.