Lower Bounds on the Number of Rational Points of Jacobians over Finite Fields and Application to Algebraic Function Fields in Towers

Moscow Mathematical Journal ◽

10.17323/1609-4514-2015-15-3-425-433 ◽

2015 ◽

Vol 15 (3) ◽

pp. 425-433 ◽

Author(s):

S. Ballet ◽

R. Rolland ◽

S. Tutdere

Keyword(s):

Finite Fields ◽

Lower Bounds ◽

Function Fields ◽

Algebraic Function ◽

Rational Points ◽

Algebraic Function Fields

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ALGEBRAIC FUNCTION FIELDS OVER FINITE FIELDS

Coding Theory and Cryptology - Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore ◽

10.1142/9789812388841_0007 ◽

2002 ◽

pp. 259-282 ◽

Author(s):

Harald Niederreiter

Keyword(s):

Finite Fields ◽

Function Fields ◽

Algebraic Function ◽

Algebraic Function Fields

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Algebraic function fields over finite fields with many rational places

IEEE Transactions on Information Theory ◽

10.1109/18.476212 ◽

1995 ◽

Vol 41 (6) ◽

pp. 1548-1563 ◽

Author(s):

A. Garcia ◽

H. Stichtenoth

Keyword(s):

Finite Fields ◽

Function Fields ◽

Algebraic Function ◽

Rational Places ◽

Algebraic Function Fields

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New Linear Codes and Algebraic Function Fields Over Finite Fields

IEEE Transactions on Information Theory ◽

10.1109/tit.2007.909125 ◽

2007 ◽

Vol 53 (12) ◽

pp. 4822-4825 ◽

Author(s):

Chaoping Xing ◽

Sze Ling Yeo

Keyword(s):

Finite Fields ◽

Linear Codes ◽

Function Fields ◽

Algebraic Function ◽

Algebraic Function Fields

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A note on divisor class groups of degree zero of algebraic function fields over finite fields

Finite Fields and Their Applications ◽

10.1016/s1071-5797(02)00004-7 ◽

2003 ◽

Vol 9 (1) ◽

pp. 129-133

Author(s):

Ferruh Özbudak

Keyword(s):

Finite Fields ◽

Function Fields ◽

Algebraic Function ◽

Degree Zero ◽

Class Groups ◽

Divisor Class ◽

Algebraic Function Fields

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Algebraic function fields of one variable over finite fields are stable

Israel Journal of Mathematics ◽

10.1007/bf02764972 ◽

1989 ◽

Vol 68 (1) ◽

pp. 102-108 ◽

Author(s):

Wulf-Dieter Geyer

Keyword(s):

Finite Fields ◽

Function Fields ◽

Algebraic Function ◽

Algebraic Function Fields

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β-Expansions in algebraic function fields over finite fields

Finite Fields and Their Applications ◽

10.1016/j.ffa.2005.08.008 ◽

2007 ◽

Vol 13 (2) ◽

pp. 394-410 ◽

Author(s):

Klaus Scheicher

Keyword(s):

Finite Fields ◽

Function Fields ◽

Algebraic Function ◽

Algebraic Function Fields

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Lower bounds on the class number of algebraic function fields defined over any finite field

Journal de Théorie des Nombres de Bordeaux ◽

10.5802/jtnb.809 ◽

2012 ◽

Vol 24 (3) ◽

pp. 505-540

Author(s):

Stéphane Ballet ◽

Robert Rolland

Keyword(s):

Finite Field ◽

Lower Bounds ◽

Class Number ◽

Function Fields ◽

Algebraic Function ◽

Algebraic Function Fields

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Diophantine Undecidability over Algebraic Function Fields over Finite Fields of Constants

Journal of Number Theory ◽

10.1006/jnth.1996.0080 ◽

1996 ◽

Vol 58 (2) ◽

pp. 317-342 ◽

Author(s):

Alexandra Shlapentokh

Keyword(s):

Finite Fields ◽

Function Fields ◽

Algebraic Function ◽

Algebraic Function Fields ◽

Diophantine Undecidability

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Effective Bounds on Class Number and Estimation for any Step of Towers of Algebraic Function Fields over Finite Fields

Moscow Mathematical Journal ◽

10.17323/1609-4514-2015-15-4-653-677 ◽

2015 ◽

Vol 15 (4) ◽

pp. 653-677

Author(s):

S. Ballet ◽

R. Rolland ◽

S. Tutdere

Keyword(s):

Finite Fields ◽

Class Number ◽

Function Fields ◽

Algebraic Function ◽

Algebraic Function Fields

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Low-discrepancy sequences obtained from algebraic function fields over finite fields

Acta Arithmetica ◽

10.4064/aa-72-3-281-298 ◽

1995 ◽

Vol 72 (3) ◽

pp. 281-298 ◽

Author(s):

Harald Niederreiter ◽

Chaoping Xing

Keyword(s):

Finite Fields ◽

Function Fields ◽

Algebraic Function ◽

Low Discrepancy Sequences ◽

Algebraic Function Fields

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