Explicit construction of codes on an asymptotically bad tower of function fields

2003 ◽  
Author(s):  
Wei-Hsin Gu ◽  
Chung-Chin Lu
Keyword(s):  
Function Fields ◽  
Explicit Construction ◽  
Tower Of Function Fields

scholarly journals Weierstrass Semigroups in an Asymptotically Good Tower of Function Fields

1998 ◽  
Vol 4 (4) ◽  
pp. 381-392 ◽  
Author(s):  
Ruud Pellikaan ◽  
Henning Stichtenoth ◽  
Fernando Torres
Keyword(s):  
Function Fields ◽  
Weierstrass Semigroups ◽  
Tower Of Function Fields

scholarly journals Bases for Riemann–Roch Spaces of One-Point Divisors on an Optimal Tower of Function Fields

2012 ◽  
Vol 58 (5) ◽  
pp. 2589-2598 ◽  
Author(s):  
Francesco Noseda ◽  
Gilvan Oliveira ◽  
Luciane Quoos
Keyword(s):  
Function Fields ◽  
Tower Of Function Fields

scholarly journals ON INVARIANTS OF TOWERS OF FUNCTION FIELDS OVER FINITE FIELDS

2013 ◽  
Vol 12 (04) ◽  
pp. 1250190 ◽  
Author(s):  
FLORIAN HESS ◽  
HENNING STICHTENOTH ◽  
SEHER TUTDERE
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Function Fields ◽  
Finite Extension ◽  
Towers Of Function Fields ◽  
Asymptotic Number ◽  
Tower Of Function Fields

In this paper, we consider a tower of function fields [Formula: see text] over a finite field 𝔽q and a finite extension E/F0 such that the sequence [Formula: see text] is a tower over the field 𝔽q. Then we study invariants of [Formula: see text], that is, the asymptotic number of the places of degree r in [Formula: see text], for any r ≥ 1, if those of [Formula: see text] are known. We first give a method for constructing towers of function fields over any finite field 𝔽q with finitely many prescribed invariants being positive. For q a square, we prove that with the same method one can also construct towers with at least one positive invariant and certain prescribed invariants being zero. Our method is based on explicit extensions. Moreover, we show the existence of towers over a finite field 𝔽q attaining the Drinfeld–Vladut bound of order r, for any r ≥ 1 with qr a square (see [1, Problem-2]). Finally, we give some examples of non-optimal recursive towers with all but one invariants equal to zero.

On the splitting of places in a tower of function fields meeting the Drinfeld-Vladut bound

2001 ◽  
Vol 47 (4) ◽  
pp. 1613-1619 ◽  
Author(s):  
I. Aleshnikov ◽  
P.V. Kumar ◽  
K.W. Shum ◽  
H. Stichtenoth
Keyword(s):  
Function Fields ◽  
Tower Of Function Fields

On evaluation codes coming from a tower of function fields

2018 ◽  
Vol 89 ◽  
pp. 121-128
Author(s):  
Cícero Carvalho ◽  
María Chara ◽  
Luciane Quoos
Keyword(s):  
Function Fields ◽  
Evaluation Codes ◽  
Tower Of Function Fields

A sequence of one-point codes from a tower of function fields

2006 ◽  
Vol 41 (3) ◽  
pp. 251-267 ◽  
Author(s):  
Takehiro Hasegawa ◽  
Shoichi Kondo ◽  
Hidekazu Kurusu
Keyword(s):  
Function Fields ◽  
Tower Of Function Fields

scholarly journals Cusp eigenforms and the hall algebra of an elliptic curve

2013 ◽  
Vol 149 (6) ◽  
pp. 914-958 ◽  
Author(s):  
Dragos Fratila
Keyword(s):  
Tensor Product ◽  
Finite Field ◽  
Elliptic Curve ◽  
Function Fields ◽  
Hecke Algebras ◽  
Explicit Construction ◽  
Hall Algebra ◽  
Langlands Correspondence ◽  
Hall Algebras ◽  
Compositio Math

AbstractWe give an explicit construction of the cusp eigenforms on an elliptic curve defined over a finite field, using the theory of Hall algebras and the Langlands correspondence for function fields and ${\mathrm{GL} }_{n} $. As a consequence we obtain a description of the Hall algebra of an elliptic curve as an infinite tensor product of simpler algebras. We prove that all these algebras are specializations of a universal spherical Hall algebra (as defined and studied by Burban and Schiffmann  [On the Hall algebra of an elliptic curve I, Preprint (2005), arXiv:math/0505148 [math.AG]] and Schiffmann and Vasserot [The elliptic Hall algebra, Cherednik Hecke algebras and Macdonald polynomials, Compositio Math. 147 (2011), 188–234]).

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