Reed-Muller codes and supersingular curves. I

Gerard Van der Geer; Marcel Van der Vlugt

Compositio Mathematica (1992)

  • Volume: 84, Issue: 3, page 333-367
  • ISSN: 0010-437X

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Van der Geer, Gerard, and Van der Vlugt, Marcel. "Reed-Muller codes and supersingular curves. I." Compositio Mathematica 84.3 (1992): 333-367. <http://eudml.org/doc/90187>.

@article{VanderGeer1992,
author = {Van der Geer, Gerard, Van der Vlugt, Marcel},
journal = {Compositio Mathematica},
keywords = {groups of automorphisms; error correcting BCH-codes; linearized polynomial; hyperelliptic curves; number of rational points; Jacobians; Reed-Muller codes},
language = {eng},
number = {3},
pages = {333-367},
publisher = {Kluwer Academic Publishers},
title = {Reed-Muller codes and supersingular curves. I},
url = {http://eudml.org/doc/90187},
volume = {84},
year = {1992},
}

TY - JOUR
AU - Van der Geer, Gerard
AU - Van der Vlugt, Marcel
TI - Reed-Muller codes and supersingular curves. I
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 84
IS - 3
SP - 333
EP - 367
LA - eng
KW - groups of automorphisms; error correcting BCH-codes; linearized polynomial; hyperelliptic curves; number of rational points; Jacobians; Reed-Muller codes
UR - http://eudml.org/doc/90187
ER -

References

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  1. [Be] Berlekamp, E.R.: The weight enumerators for certain subcodes of the second order Reed-Muller codes. Info. and Control17 (1970), 485-500. Zbl0211.51304MR290857
  2. [H-D] Hasse, H., Davenport, H.: Die Nullstellen der Kongruenzzetafunktion in gewissen zyklischen Fällen. Journal f.d.r.u.a. Math.172 (1934), 151-182. Zbl0010.33803JFM60.0913.01
  3. [Hu] Huppert, B.: Endliche Gruppen I. Grundlehren der Math. Wiss.134. Springer-Verlag, Berlin, 1967. Zbl0217.07201MR224703
  4. [Jo] Joly, J.- R.: Equations et variétés algébriques sur un corps fini. Ens. Math.19 (1973), 1-117. Zbl0282.14005MR327723
  5. [MacW-S] MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-correcting Codes. North-Holland, Amsterdam, 1983. Zbl0657.94010
  6. [Mu1] Mumford, D.: Prym Varieties I, in Contributions to Analysis, pp. 325-350. Academic Press, London, New York, 1974. Zbl0299.14018MR379510
  7. [Mu2] Mumford, D.: Abelian Varieties. Oxford University Press1974. Zbl0326.14012
  8. [Se] Serre, J-P.: Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini. C.R. Acad. Sci. Paris296, Série I (1983), 397-402. Zbl0538.14015MR703906
  9. [T] Tate, J.: Endomorphisms of abelian varieties over finite fields. Invent. Math.2 (1966), 134-144. Zbl0147.20303MR206004

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