ON ASYMPTOTICALLY OPTIMAL TOWERS OVER QUADRATIC FIELDS RELATED TO GAUSS HYPERGEOMETRIC FUNCTIONS

DOI10.1142/S1793042110003344zbMath1239.11132OpenAlexW2043537222MaRDI QIDQ4929862

Takehiro Hasegawa

Publication date: 24 September 2010

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042110003344

zbMATH Keywords

hypergeometric functionsfinite fieldsrational pointstowers of function fieldsDeuring's polynomial

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Classical hypergeometric functions, ({}_2F_1) (33C05) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (4)

Towers of function fields over finite fields corresponding to elliptic modular curves ⋮ Some remarks on superspecial and ordinary curves of low genus ⋮ Remarks on a paper by El-Guindy and Papanikolas ⋮ Logarithmic-type and exponential-type hypergeometric functions for function fields

Cites Work

• On the construction of tame towers over finite fields
• The Atkin orthogonal polynomials for congruence subgroups of low levels
• On towers and composita of towers of function fields over finite fields
• On the asymptotic behaviour of some towers of function fields over finite fields
• Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial
• A sequence of one-point codes from a tower of function fields
• Explicit identities for invariants of elliptic curves
• Weierstrass semigroups and codes from a quotient of the Hermitian curve
• Asymptotically good towers and differential equations
• Modular differential equations of second order with regular singularities at elliptic points for $SL_2(\mathbb {Z})$
• Explicit Constructions of Algebraic-Geometric Codes
• Codes From the Suzuki Function Field
• Transitive and self-dual codes attaining the Tsfasman-Vla/spl breve/dut$80-Zink bound
• An explicit construction of a sequence of codes attaining the Tsfasman-Vladut-Zink bound. The first steps
• Towers of function fields and iterated means
• On the splitting of places in a tower of function fields meeting the Drinfeld-Vladut bound
• A low-complexity algorithm for the construction of algebraic-geometric codes better than the Gilbert-Varshamov bound
• Codes on Garcia-Stichtenoth curves with true distance greater than Feng-Rao distance
• On the number of correctable errors of the Feng-Rao decoding algorithm for AG codes

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