Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
DE
EN
Books
Journals
Events
Topic Page
Marketing
Log in
Learn more about individual access
Request company access
Electric Powertrains and Energy Systems 2025 | 26 + 27 March 2025

19th International MTZ Congress on Future Powertrains

Take this opportunity to attend the conference. Experts from the automotive industry, energy providers, and grid operators will meet up with representatives from politics and science to discuss important topics for this sector.
EXTENDED SEARCH
Log in
Top
Applicable Algebra in Engineering, Communication and Computing
Published in:

20-08-2022 | Original Paper

A note on subtowers and supertowers of recursive towers of function fields

Authors: M. Chara, H. Navarro, R. Toledano

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 6/2023

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper we study the problem of constructing non-trivial subtowers and supertowers of recursive towers of function fields over finite fields.
previous article Construction of constant dimension codes via improved inserting construction

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Footnotes
1
This means that H is irreducible over an algebraic closure of \(\mathbb {F}_q\) and that \(H(S,T)=H(T,S).\)
 
Literature
1.
Anbar, N., Beelen, P., Nguyen, N.: The exact limit of some cubic towers. In: Arithmetic, Geometry, Cryptography and Coding Theory. Contemporary Mathematics, vol. 686, pp. 1–15 (2017)
2.
Bassa, A., Beelen, P., Garcia, A., Stichtenoth, H.: Towers of function fields over non-prime finite fields. Mosc. Math. J. 15(1), 181–210 (2015)MathSciNetMATH
3.
Bezerra, J., Garcia, A.: A tower with non-Galois steps which attains the Drinfeld–Vladut bound. J. Number Theory 106(1), 142–154 (2004)MathSciNetCrossRefMATH
4.
5.
Bezerra, J., Garcia, A., Stichtenoth, H.: An explicit tower of function fields over cubic finite fields and Zink’s lower bound. J. Reine Angew. Math. 589, 159–199 (2005)MathSciNetCrossRefMATH
6.
Beelen, P., Garcia, A., Stichtenoth, H.: Towards a classification of recursive towers of function fields over finite fields. Finite Fields Appl. 12(1), 56–77 (2006)MathSciNetCrossRefMATH
7.
8.
Dummit, D., Foote, R.: Abstract Algebra, 3rd edn. Wiley, New York (2004)MATH
9.
Garcia, A., Stichtenoth, H.: A tower of Artin–Schreier extensions of function fields attaining the Drinfeld–Vladut bound. Invent. Math. 121, 211–222 (1995)MathSciNetCrossRefMATH
10.
Garcia, A., Stichtenoth, H.: On the asymptotic behaviour of some towers of function fields over finite fields. J. Number Theory 61, 248–273 (1996)MathSciNetCrossRefMATH
11.
Garcia, A., Stichtenoth, H.: Explicit towers of function fields over finite fields. In: Topics in Geometry, Coding Theory and Cryptography, Volume 6 of Algebra and Applications. Springer, Dordrecht, pp. 1–58 (2007)
12.
Garcia, A., Stichtenoth, H., Rück, H.: On tame towers over finite fields. J. Reine Angew. Math. 557, 53–80 (2003)MathSciNetMATH
13.
Ihara, Y.: Some remarks on the number of rational points of algebraic curves over finite fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28(3), 721–724 (1982), (1981)
14.
Maharaj, H., Wulftange, J.: On the construction of tame towers over finite fields. J. Pure Appl. Algebra 199(1–3), 197–218 (2005)MathSciNetCrossRefMATH
15.
Stichtenoth, H.: Algebraic Function Fields and Codes. GTM 254, 2nd edn. Springer, Berlin (2009)CrossRefMATH
16.
Zieve, M.: An equality between two towers over cubic fields. arXiv:0905.4921 (2009)
Metadata
Title
A note on subtowers and supertowers of recursive towers of function fields
Authors
M. Chara
H. Navarro
R. Toledano
Publication date
20-08-2022
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 6/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-022-00576-1

Other articles of this Issue 6/2023

On symbol-pair distances of repeated-root constacyclic codes of length over and MDS symbol-pair codes

  • Original Paper

Two-valued cross correlation distributions between binary m sequences and their decimation sequences

  • Original Paper

Interleavings and matchings as representations

  • Original Paper

Best Paper Award in Memory of Jacques Calmet

  • Announcement

Quantum MDS and synchronizable codes from cyclic codes of length over

  • Original Paper

LCD codes from equitable partitions of association schemes

  • Original Paper

Premium Partner

    Image Credits