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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Construction of global function fields from linear codes and vice versa


Authors: Chaoping Xing and Sze Ling Yeo
Journal: Trans. Amer. Math. Soc. 361 (2009), 1333-1349
MSC (2000): Primary 11G20, 14H05, 11R60
Published electronically: October 14, 2008
MathSciNet review: 2457401
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Abstract: We introduce a new connection between linear codes and global function fields, which in turn allows us to construct new global function fields with improved lower bounds on the number of rational places. The genus and number of rational places of subfields of certain families of cyclotomic function fields are given as well.


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Additional Information

Chaoping Xing
Affiliation: School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637616, Republic of Singapore.
Email: xingcp@ntu.edu.sg

Sze Ling Yeo
Affiliation: Systems & Security Department (SSD), Institute for Infocomm Research (I2R), Singapore 119613, Republic of Singapore.
Email: slyeo@i2r.a-star.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04710-7
PII: S 0002-9947(08)04710-7
Received by editor(s): September 1, 2005
Received by editor(s) in revised form: January 4, 2007
Published electronically: October 14, 2008
Additional Notes: The first author is the corresponding author.
The first author was partially supported by the National Scientific Research Project 973 of China 2004CB318000.
Article copyright: © Copyright 2008 American Mathematical Society