Constructing function fields¶with many rational places via the Carlitz module

Max Gebhardt

doi:10.1007/s002290100226

Constructing function fields¶with many rational places via the Carlitz module

manuscripta mathematica ◽

10.1007/s002290100226 ◽

2002 ◽

Vol 107 (1) ◽

pp. 89-99

Author(s):

Max Gebhardt

Keyword(s):

Function Fields ◽

Rational Places ◽

Carlitz Module

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Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places

Acta Arithmetica ◽

10.4064/aa-79-1-59-76 ◽

1997 ◽

Vol 79 (1) ◽

pp. 59-76 ◽

Cited By ~ 15

Author(s):

Harald Niederreiter ◽

Chaoping Xing

Keyword(s):

Function Fields ◽

Global Function ◽

Global Function Fields ◽

Rational Places ◽

Class Fields

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GLOBAL FUNCTION FIELDS WITH MANY RATIONAL PLACES OVER THE QUINARY FIELD

Demonstratio Mathematica ◽

10.1515/dema-1997-0421 ◽

1997 ◽

Vol 30 (4) ◽

pp. 919-930 ◽

Cited By ~ 4

Author(s):

Harald Niederreiter ◽

Chaoping Xing

Keyword(s):

Function Fields ◽

Global Function ◽

Global Function Fields ◽

Rational Places

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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 ◽

Cited By ~ 24

Author(s):

A. Garcia ◽

H. Stichtenoth

Keyword(s):

Finite Fields ◽

Function Fields ◽

Algebraic Function ◽

Rational Places ◽

Algebraic Function Fields

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Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fields

Journal of Number Theory ◽

10.1016/j.jnt.2014.05.012 ◽

2014 ◽

Vol 145 ◽

pp. 181-193 ◽

Cited By ~ 1

Author(s):

Nguyen Ngoc Dong Quan

Keyword(s):

Function Fields ◽

Carlitz Module ◽

Mersenne Primes ◽

Prime Elements

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Asymptotics for the genus and the number of rational places in towers of function fields over a finite field

Finite Fields and Their Applications ◽

10.1016/j.ffa.2005.04.004 ◽

2005 ◽

Vol 11 (3) ◽

pp. 434-450 ◽

Cited By ~ 2

Author(s):

Arnaldo Garcia ◽

Henning Stichtenoth

Keyword(s):

Finite Field ◽

Function Fields ◽

Rational Places ◽

Towers Of Function Fields

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Function Fields with Many Rational Places

Rational Points on Curves over Finite Fields ◽

10.1017/cbo9781107325951.005 ◽

2001 ◽

pp. 76-121

Keyword(s):

Function Fields ◽

Rational Places

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Low-Discrepancy Sequences and Global Function Fields with Many Rational Places

Finite Fields and Their Applications ◽

10.1006/ffta.1996.0016 ◽

1996 ◽

Vol 2 (3) ◽

pp. 241-273 ◽

Cited By ~ 97

Author(s):

Harold Niederreiter ◽

Chaoping Xing

Keyword(s):

Function Fields ◽

Global Function ◽

Global Function Fields ◽

Low Discrepancy Sequences ◽

Rational Places

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Bounding the number of Fq-rational places in algebraic function fields using Weierstrass semigroups

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2008.11.013 ◽

2009 ◽

Vol 213 (6) ◽

pp. 1152-1156 ◽

Cited By ~ 9

Author(s):

Olav Geil ◽

Ryutaroh Matsumoto

Keyword(s):

Function Fields ◽

Algebraic Function ◽

Rational Places ◽

Algebraic Function Fields ◽

Weierstrass Semigroups

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Explicit global function fields over the binary field with many rational places

Acta Arithmetica ◽

10.4064/aa-75-4-383-396 ◽

1996 ◽

Vol 75 (4) ◽

pp. 383-396 ◽

Cited By ~ 12

Author(s):

Harald Niederreiter ◽

Chaoping Xing

Keyword(s):

Function Fields ◽

Global Function ◽

Binary Field ◽

Global Function Fields ◽

Rational Places

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Some Artin–Schreier type function fields over finite fields with prescribed genus and number of rational places

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2006.08.007 ◽

2007 ◽

Vol 210 (1) ◽

pp. 113-135 ◽

Cited By ~ 14

Author(s):

Emrah Çakçak ◽

Ferruh Özbudak

Keyword(s):

Finite Fields ◽

Function Fields ◽

Type Function ◽

Rational Places

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