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Explicit Construction of Good Towers of Function Fields
Nhut Nguyen
Advisor: Prof. Peter Beelen joint work with Alp Bassa
Technical University of Denmark
Motivation
Explicit Construction of Good Towers of Function Fields Nhut Nguyen - - PowerPoint PPT Presentation
Explicit Construction of Good Towers of Function Fields Nhut Nguyen - - PowerPoint PPT Presentation
Explicit Construction of Good Towers of Function Fields Nhut Nguyen Advisor: Prof. Peter Beelen joint work with Alp Bassa Technical University of Denmark Motivation Asymptotic Code Bounds ( N ) Figure: For squares q 49 , there
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Asymptotic Code Bounds (N → ∞)
Figure: For squares q ≥ 49, there exists Algebraic Geometric Codes
- ver GF(q) beating Gilbert-Varshamov Bound in some interval.
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Goal
Explicit construction of algebraic curves having many points
- ver a finite field.
Result
A procedure (algorithm) to produce explicit equations for such good sequences of curves.
Method
Drinfeld modular theory. x4
n+1x3 n + x4 n+1x2 n + x4 n+1xn + x3 n+1x2 n + x3 n+1xn + x3 n+1
+x2
n+1xn + x2 n+1 + xn+1x3 n + xn+1 + x4 n = 0.
(1)
Figure: An example of our optimal tower over GF(16).
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Obrigado!
SPCodingSchool BBQ, Campinas, Brazil, 23 Jan 2015.