Construction of global function fields from linear codes and vice versa
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- by Chaoping Xing and Sze Ling Yeo PDF
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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.References
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Additional Information
- Chaoping Xing
- Affiliation: School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637616, Republic of Singapore.
- MR Author ID: 264368
- 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
- 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. - © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 361 (2009), 1333-1349
- MSC (2000): Primary 11G20, 14H05, 11R60
- DOI: https://doi.org/10.1090/S0002-9947-08-04710-7
- MathSciNet review: 2457401