Henning Stichtenoth
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  • Henning Stichtenoth

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E-Mail
henningsabanciunivedu
Phone
(216) 483 9581
Personal Web
Title
Emeritus Faculty Member
Jobs
Instructor
Education
Studies of Mathematics in Hannover and Heidelberg (Germany),
PhD in Mathematics, University of Heidelberg, 1972
Areas of Interest
Research areas: Algebraic Function Fields and Curves, in particular in positive characteristic, Coding Theory
Publications
  • Article
    Ben-Sasson, Eli and Kaplan, Yohay and Kopparty, Swastik and Meir, Or and Stichtenoth, Henning (2016) "Constant rate PCPs for circuit-SAT with sublinear query complexity", Journal of the ACM, Vol.63, No.4, 1-57 (SCI)
    Ateş, Leyla and Stichtenoth, Henning (2016) "A note on short vectors in lattices from function fields", Finite Fields and Their Applications, Vol.39, 264-271 (SCI)
    Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2015) "Towers of function fields over non-prime finite fields", Moscow Mathematical Journal, Vol.15, No.1, 1-29 (SCI)
    Stichtenoth, Henning and Tutdere, Seher (2015) "Quadratic recursive towers of function fields over F-2", Turkish Journal of Mathematics, Vol.39, No.5, 665-682 (SCI)
    Stichtenoth, Henning (2014) "A note on composed products of polynomials over finite fields", Designs, Codes, and Cryptography, Vol.73, No.1, 27-32 (SCI)
    Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2014) "An improvement of the Gilbert-Varshamov bound over nonprime fields", IEEE Transactions on Information Theory, Vol.60, No.7, 3859-3861 (SCI)
    Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2014) "Galois towers over non-prime finite fields", Acta Arithmetica, Vol.164, No.2, 163-179 (SCI)
    Anbar, Nurdagül and Stichtenoth, Henning (2013) "Curves of every genus with a prescribed number of rational points", Bulletin of the Brazilian Mathematical Society, Vol.44, No.2, 173-193 (SCI)
    Hess, Florian and Stichtenoth, Henning and Tutdere, Seher (2013) "On invariants of towers of function fields over finite fields", Journal of Algebra and Its Applications, Vol.12, No.4 (SCI)
    Anbar, Nurdagül and Stichtenoth, Henning (2013) "On the number of rational points of curves over finite fields", Electronic Notes in Discrete Mathematics, Vol.40, 21-26 (OTHER)
    Güneri, Cem and Özdemir, Mehmet and Stichtenoth, Henning (2013) "The automorphism group of the generalized Giulietti-Korchmaros function field", Advances in Geometry, Vol.13, No.2, 369-380 (SCI)
    Stichtenoth, Henning and Topuzoğlu, Alev (2012) "Factorization of a class of polynomials over finite fields", Finite Fields and Their Applications, Vol.18, No.1, 108-122 (SCI)
    Stichtenoth, Henning (2011) "Curves with a prescribed number of rational points", Finite Fields and Their Applications, Vol.17, No.6, 552-559 (SCI)
    Garcia, Arnaldo and Güneri, Cem and Stichtenoth, Henning (2010) "A generalization of the Giulietti-Korchmaros maximal curve", Advances in Geometry, Vol.10, No.3, 427-434 (SCI)
    Anbar, Nurdagül and Stichtenoth, Henning and Tutdere, Seher (2009) "On ramification in the compositum of function fields", Bulletin of the Brazilian Mathematical Society, Vol.40, No.4, 539-552 (SCI)
    Güneri, Cem and Stichtenoth, Henning and Taşkın, İhsan (2009) "Further improvements on the designed minimum distance of algebraic geometry codes", Journal of Pure and Applied Algebra, Vol.213, No.1, 87-97 (SCI)
    Bassa, Alp and Garcia, Arnaldo and Stichtenoth, Henning (2008) "A new tower over cubic finite fields", Moscow Mathematical Journal, Vol.8, No.3, 401-418 (SCI)
    Bassa, Alp and Stichtenoth, Henning (2007) "A simplified proof for the limit of a tower over a cubic finite field", Journal of Number Theory, Vol.123, No.1, 154-169 (SCI)
    Garcia, Arnaldo and Stichtenoth, Henning (2006) "Some Artin-Schreier towers are easy", Moscow Mathematical Journal, Vol.5, No.4 (SCI)
    Stichtenoth, Henning (2006) "Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound", IEEE Transactions On Information Theory, Vol.52, No.5, 2218-2224 (SCI)
    Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2006) "Towards a classification of recursive towers of function fields over finite fields", Finite Fields and Their Applications, Vol.12, No.1, 56-77 (SCI)
    Garcia, Arnaldo and Stichtenoth, Henning (2006) "A maximal curve which is not a Galois subcover of the Hermitian curve", Bulletin of the Brazilian Mathematical Society, Vol.37, No.1, 139-152 (SCI)
    Bezerra, J. and Garcia, Arnaldo and Stichtenoth, Henning (2005) "An explicit tower of function fields over cubic finite fields and Zink`s lower bound", Journal fur die Reine und Angewandte Mathematik, Vol.589, 159-199 (SCI)
    Ling, San and Stichtenoth, Henning and Yang, Siman (2005) "A class of Artin-Schreier towers with finite genus", Bulletin of the Brazilian Mathematical Society, Vol.36, No.3, 393-401 (SCI)
    Stichtenoth, Henning and Xing, Chaoping P. (2005) "Excellent nonlinear codes from algebraic function fields", IEEE Transactions On Information Theory, Vol.51, No.11, 4044-4046 (SCI)
    Garcia, Arnaldo and Stichtenoth, Henning (2005) "Asymptotics for the genus and the number of rational places in towers of function fields over a finite field", Finite Fields and Their Applications, Vol.11, No.3, 434-450 (SCI)
    Banks, William D. and Luca, Florian and Shparlinski, Igor E. and Stichtenoth, Henning (2005) "On the value set of n! modulo a prime", Turkish Journal of Mathematics, Vol.29, No.2, 169-174 (NA)
    Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2005) "On ramification and genus of recursive towers", Portugaliae Math, Vol.62, No.2, 1-13 (NA)
    Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2004) "On towers of function fields of Artin-Schreier type", Bulletin of the Brazilian Mathematical Society, Vol.35, No.2, 151-164 (SCI)
  • Book
    Stichtenoth, Henning, Algebraic function fields and codes, Berlin-Heidelberg: Springer Verlag 2009
  • Book Section / Chapter
    Garcia, Arnaldo and Stichtenoth, Henning, "Introduction to function fields and curves", Handbook of Finite Fields, Mullen, Gary L. and Panario, Daniel (eds.), Boca Raton, London, New York: CRC Press, June 2013
    Garcia, Arnaldo and Stichtenoth, Henning, "Rational points on curves", Handbook of Finite Fields, Mullen, Gary L. and Panario, Daniel (eds.), Boca Raton, London, New York: CRC Press, June 2013
    Garcia, Arnaldo and Stichtenoth, Henning, "Towers", Handbook of Finite Fields, Mullen, Gary L. and Panario, Daniel (eds.), Boca Raton, London, New York: CRC Press, June 2013
    Garcia, Arnaldo and Stichtenoth, Henning, "On the galois closure of towers", Recent Trends in Coding Theory and Its Applications, Li, Wen-Ching Winnie (ed.), Rhode Island, USD: American Mathematical Society 2007, 83-94
    Stichtenoth, Henning and Garcia, Arnaldo, "Explicit towers of function fields over finite fields", Topics in geometry, coding theory and cryptography, Dordrecht: Springer , November 2006, 1-58
  • Papers in Conference Proceedings
    Garcia, Arnaldo and Stichtenoth, Henning, "A note on a maximal curve", Kohel, David R. and Rolland, Robert (eds.), 12th Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, Providence, RI: AMS (American Mathematical Society) 2010, 55-58
    Stichtenoth, Henning, "Recursive towers of function fields over finite fields", Hasan, M. Anwar and Helleseth, Tor (eds.), 3rd International Workshop on Arithmetic of Finite Fields (WAIFI 2010), Berlin, Germany: Springer 2010, 1-6
  • Volumes Edited / Special Issues
    Garcia, Arnaldo and Stichtenoth, Henning, Topics in geometry, coding theory and cryptography, Berlin, New York: Springer, December 2006
  • Before SU Publications

    I. Books and Edited Volumes

    [6] Finite Fields and Applications (ed., with G. L. Mullen and A. Poli). Proceedings

    of the 7th International Conference Fq7, Toulouse 2003, Springer Lecture

    Notes in Computer Science 2948.

    [5] Finite Fields with Applications to Coding Theory, Cryptography and Related

    Areas (ed., with G. Mullen and H. Tapia-Recillas), Proceedings of the 6th International

    Conference on Finite Fields and Applications, Springer-Verlag, Berlin,

    (2002).

    [4] Coding Theory, Cryptography and Related Areas (ed., with J. Buchmann, T.

    H_holdt and H. Tapia-Recillas), Proceedings of the Conference in Guanajuato,

    Mexico, 1998. Springer Verlag Berlin (2000).

    [3] Algebraic Function Fields and Codes. Springer Universitext (1993), ca. 260

    pp.

    [2] Coding Theory and Algebraic Geometry (ed., with M. A. Tsfasman). Springer

    Lecture Notes in Mathematics 1518 (1991).

    [1] Algebraische Funktionenkorper einer Variablen. Vorlesungen aus dem Fachbereich

    Mathematik der Universitat Essen (1978), 120 pp.

     

    II.  Research Articles in Journals (SCI)

    [55] (with A. Bassa) A simplified proof for the limit of a tower over a cubic finite

    field. In: J. Number Th. 123 (2007), 154-169.

    [54] Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound,

    IEEE Trans. Inform. Th. 52 (2006), 2218-2224.

    [53] (with A. Garcia) A maximal curve which is not a Galois subcover of the

    Hermitian curve. Bull. Braz. Math. Soc. 37 (2006), 139-152.

    [52] (with P. Beelen and A. Garcia) Towards a classification of recursive towers

    of function fields. Finite Fields Appl. 12 (2006), 56-77.

    [51] (with A. Garcia) Some Artin-Schreier towers are easy. Moscow Math. J. 5

    (2005), 767-774.

    [50] (with C. P. Xing) Excellent non-linear codes from algebraic function fields.

    IEEE Trans. Inform. Theory 51 (2005), 4044-4046.

    [49] (with J. Bezerra and A. Garcia) An explicit tower of function fields over cubic

    finite fields and Zink's lower bound. J. Reine Angew. Math. 589 (2005), 159-199.

    [48] (with S. Ling and S. Yang) A class of Artin-Schreier towers with finite genus.

    Bull. Braz. Math. Soc. 36 (2005), 393-401.

    [47] (with A. Garcia) Asymptotics for the genus and the number of rational places

    in towers of function fields over a finite field. Finite Fields Appl. 11 (2005), 434-

    450.

    [46] (with P. Beelen and A. Garcia) On ramification and genus of recursive towers.

    Portugal. Math. 62 (2005), 231-243.

    [45] (with W. D. Banks, F. Luca and I. E. Shparlinski) On the value set of n!

    modulo a prime. Turk. J. Math. 29 (2005), 169-174.

    [44] (with P. Beelen and A. Garcia) On towers of function fields of Artin-Schreier

    type. Bull Braz. Math. Soc. 35 (2004), 151-164.

    [43] (with F. Ozbudak) Constructing linear unequal protection codes from algebraic

    curves. IEEE Trans. Inform. Th. 49 (2003), 1523-1527.

    [42] (with A. Garcia) On Tame Towers over Finite Fields. J. Reine Angew. Math.

    557 (2003), 53 - 80.

    [41] (with F. Ozbudak) Note on Niederreiter-Xing's propagation rule for linear

    codes. Applic. Algebra in Engin., Commun. and Comp. 13 (2002), 53 - 56.

    [40] (with I. Aleschnikov, V. Deolalikar, P. V. Kumar and K. Shum) A Low-

    Complexity Algorithm for Construction of Algebraic Geometric Codes better than

    the Gilbert-Varshamov-Bound. IEEE Trans. Inform. Th. 47 (2001), 2225 - 2241.

    1999), D. Jungnickel and H. Niederreiter (eds.), 14 - 24, Springer Verlag, 2001.

    [39] (with I. Aleschnikov, P. V. Kumar and K. Shum) On the splitting of places

    in a tower of function fields meeting the Drinfeld-Vladut bound. IEEE Trans.

    Inform. Th. 47 (2001), 1613 - 1619.

    [38] (with A. Garcia and C. P. Xing) On subfields of the Hermitian function field.

    Compositio Mathematica 120 (2000), 137 - 170.

    [37] (with F.  Ozbudak) Constructing codes from algebraic curves. IEEE Trans.

    Inform. Th. 45 (1999), 2502 - 2505.

    [36] (with A. Garcia) On Chebyshev Polynomials and Maximal Curves. Acta

    Arith. 90 (1999), 301 - 311.

    [35] (with A. Garcia) A Class of Polynomials over Finite Fields. Finite Fields

    Appl. 5 (1999), 424 - 435.

    [34] (with F. Ozbudak) Curves with many points and configurations of hyperplanes

    over finite fields. Finite Fields Appl. 5 (1999), 436 - 449.

    [33] (with R. Pellikaan and F. Torres) Weierstrass semigroups in an asymptotically

    good Tower of Function Fields. Finite Fields Appl. 4 (1998), 381 - 392.

    [32] (with A. Garcia and M. Thomas) On Towers and Composita of Towers of

    Function Fields over Finite Fields. Finite Fields Appl. 3 (1997), 257 - 274.

    [31] (with A. Garcia) On the asymptotic behaviour of some towers of function

    fields over finite fields. Journal of Number Theory, 61 (1996), 248 - 273.

    [30] (with A. Garcia) Asymptotically good towers of function fields over finite

    fields. C. R. Acad. Sci. Paris, Ser. I, 322, 1067 - 1070 (1996).

    [29] (with A. Garcia) Algebraic function fields over finite fields with many rational

    places. IEEE Trans. Inform. Th. 41, No. 6 (1995), 1548-1563.

    [28] (with A. Garcia) A tower of Artin-Schreier extensions of function fields attaining

    the Drinfeld-Vladut bound. Invent. Math. 121 (1995), 211 - 222.

    [27] (with C. P. Xing) On the structure of the divisor class group of a class of

    curves over finite fields. Arch. Math. 65 (1995), 141 - 150.

    [26] (with C. P. Xing) The genus of maximal function fields. Manuscr. Math. 86

    (1995), 217 - 224.

    [25] (with H.-G. Ruck) A Characterization of Hermitian Function Fields over Fq2 .

    J. Reine Angew. Math. 457 (1994), 185 - 188.

    [24] (with P. V. Kumar and K. Yang) On the Weight Hierarchy of Geometric

    Goppa Codes. IEEE Trans. on Inform. Th. 40 (1994), 913 - 920.

    [23] (with C. Voss) Generalized Hamming Weights of Trace Codes. IEEE Trans.

    on Inform. Th. 40 (1994), 554 - 558.

    [22] (with A. Garcia) Elementary Abelian p-Extensions of Algebraic Function

    Fields. Manuscr. Math. 72 (1991), 67-79.

    [21] (with J. P. Hansen) Group Codes on Certain Algebraic Curves with Many

    Rational Points. Applicable Algebra in Engineering, Communication and Computing

    AAECC 1 (1990), 67-77.

    [20] (with M. Kruse) Ein Analogon zum Primzahlsatz fur algebraische

    Funktionenkorper. Manuscr. Math. 69 (1990), 219-221.

    [19] On Automorphisms of Geometric Goppa Codes. J. of Algebra 130 (1990),

    113-121.

     [18] On the Dimension of Subfield Subcodes. IEEE Trans. on Inform. Th. 36

    (1990), 90-93.

    [17] (with C. Voss) Asymptotically Good Families of Subfield Subcodes of Geometric

    Goppa Codes. Geometriae Dedicata 33 (1990), 111-116.

    [16] Which Extended Goppa Codes are Cyclic? J. Comb. Theory Ser. A 51

    (1989), 205-220.

    [15] (with Y. Driencourt) A Criterion for Self-Duality of Geometric Codes. Communications in Algebra 17 (1989), 885-898.

    [14] A Note on Hermitian Codes over GF(q2). IEEE Trans. on Inform. Theory

    34 (1988), 1345-1348.

    [13] Self-dual Goppa Codes. J. Pure and Appl. Algebra 55 (1988),199-211.

    [12] (with R. Brandt) Die Automorphismengruppen hyperelliptischer Kurven.

    Manuscr. Math. 55 (1986), 83-92.

    [11] s-Erweiterungen algebraischer Funktionenkorper. Arch. Math. 43 (1984),

    27-31.

    [10] Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer

    Funktionenkorper. Math. Zeitschr. 187 (1984), 221-225.

    [9] Die Ungleichung von Castelnuovo. J. Reine Angew. Math. 348 (1984), 197-

    202.

    [8] Zur Divisorklassengruppe eines Kongruenzfunktionenkorpers. Arch. Math.

    32 (1979), 336-340.

    [7] Die Hasse-Witt-Invariante eines Kongruenzfunktionenkorpers. Arch. Math.

    33 (1979), 357-360.

    [6] p-Klassengruppen algebraischer Funktionenkorper. Arch. Math. 32 (1979),

    452-457.

    [5] Zur Konservativitat algebraischer Funktionenkorper. J. Reine Angew. Math.

    301 (1978), 30-45.

    [4] Uber das Geschlecht eines inseparablen Funktionenkorpers. Manuscr. Math.

    14 (1974), 173-182.

    [3] Algebraische Funktionenkorper einer Variablen mit Teilkorpern von beliebig

    hohem Geschlecht. Arch. Math. 25 (1974), 379-384.

    [2] Uber die Automorphismengruppe eines algebraischen Funktionenkorpers von

    Primzahlcharakteristik. Teil 2: Ein spezieller Typ von Funktionenkorpern. Arch.

    Math. 24 (1973), 615-631.

    [1] Uber die Automorphismengruppe eines algebraischen Funktionenkorpers von

    Primzahlcharakteristik. Teil 1: Eine Abschatzung der Ordnung der Automorphismengruppe.

    Arch. Math. 24 (1973), 524-544.

     

    III. Conference Proceedings et al.

    [14] Recursive Towers of Function Fields over Finite Fields, in: Arithmetic of Finite

    Fields, M.Hasan and T.Helleseth (eds.), Springer LNCS No. 6087 (2010), 1-6.

    [13] (with A. Garcia) Some Remarks on the Hasse-Arf Theorem. In: Contemp.

    Math., vol. 461 (2008), 141-146.

    [12] (with A. Garcia) On the Galois closure of towers. In: AMS/IP Studies in

    Advanced Mathematics, vol. 41 (2007), 85-92.

    [11] (with P. Beelen and A. Garcia) On towers of function fields over finite fields.

    In: Arithmetic, Geometry and Coding Theory (AGCT 2003), Semin. Congr. 11,

    Soc. Math. France, Paris (2005), 1-20.

    [10] (with W.-C. W. Li and H. Maharaj) New optimal towers of function fields

    over small finite fields. In: Proceedings of the 5th Int. Symp. on Algorithmic

    Number Theory, ANTS-5 (eds. C. Fieker and D. R. Kohel), Springer Lecture

    Notes in Computer Science 2369 (2002), 372-389.

    [9] Explicit constructions of towers of function fields with many rational places.

    In: Proceedings of the 3rd European Congress of Mathematics, Barcelona, 2000,

    Vol. 2, C. Casacuberta et al. (eds.), Progress in Mathematics 202, 219 - 224,

    Birkhauser-Verlag, 2001.

    [8] (with I. Aleschnikov, V. Deolalikar and P. V. Kumar) Towards a basis for the

    space of regular functions in a tower of function fields meeting the Drinfeld-Vladut

    bound. In: Finite Fields and their Applications (Proceedings of Fq5, Augsburg

    1999), D. Jungnickel and H. Niederreiter (eds.), 14 - 24, Springer Verlag, 2001.

    [7] (with I. Aleschnikov, P. V. Kumar and K. Shum) Integral bases in a tower of

    function fields. In: Proc. 7th Intern. Workshop on Algebraic and Combinatorial

    Coding Theory ACCT, Bansko, Bulgaria (2000), 23 - 28.

    [6] (with A. Garcia) Skew pyramids of function fields are asymptotically bad.

    In: Coding Theory, Cryptography and Related Areas (eds. J. Buchmann et al.),

    pp. 111 - 113, Springer Verlag Berlin, 2000..

    [5] The Fermat curve in characteristic p. In: Finite Fields: Theory, Applications

    and Algorithms (eds. R. C. Mullin and G. L. Mullen). AMS Contemporary

    Mathematics vol. 225 (1999), 123 - 130.

    [4] (with I. Duursma and C. Voss) Generalized Hamming Weights for Duals of

    BCH Codes, and Maximal Algebraic Function Fields. In: Arithmetic, Geometry

    and Coding Theory (eds. R. Pellikaan et al.) pp. 53 - 66. De Gruyter, Berlin-

    New York, 1996..

    [3] Algebraic-geometric codes. AMS Proc. of Symp. in Applied Math. (ed. R.

    Calderbank), Vol. 50, 139 - 152 (1995).

    [2] (with G. Frey and M. Perret) On the Different of Abelian Extensions of

    Global Fields. In `Coding Theory and Algebraic Geometry', Springer Lecture

    Notes in Mathematics (eds. M. A. Tsfasman and H. Stichtenoth) 1518 (1991),

    26-32.

    [1] Algebraic-Geometric Codes Associated to Artin-Schreier Extensions of Fq(z).

    Proceedings of the Second International Workshop on Algebraic and Combinatorial

    Coding Theory, Leningrad (1990), 203-206.

     rs of Function Fields over Finite Fields. In:

    Topics in Geometry, Coding Theory and Cryptography (eds. A. Garcia and H.

    Stichtenoth), Springer Verlag (2006), 1-58.