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Families of curves and weight distributions of codes
Author(s):
Ren\'e
Schoof
Journal:
Bull. Amer. Math. Soc.
32
(1995),
171-183.
MSC (1991):
Primary 11T71;
Secondary 14G15, 14T52
MathSciNet review:
1302786
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Additional information
References:
- [1]
- Atkin, A.O.L. and Lehner, J., Hecke operators on $\Gamma _0(m)$, Math. Ann. \textbf{185} (1970), 134--160. MR 268123
- [2]
- Deuring, M., Die Typen der Multiplikatorenringe elliptischer Funktionenk\"orper, Abh. Math. Sem. Hansischen Univ. \textbf{14} (1941), 197--272. MR 5125
- [3]
- Cohen, H., Trace des op\'erateurs de Hecke sur $\Gamma _0(N)$, S\'em. Th\'eorie Nombres \textbf{4} (1976--1977), Bordeaux. MR 562292
- [4]
- Goppa, V.G., Codes on algebraic curves, Soviet Math. Dokl. \textbf{24} (1981), 170--172. MR 628795
- [5]
- Kasami, T., \emph{Weight distributions of Bose-Chaudhuri-Hocquenghem codes \nofrills}, (Bose, R.S. and Dowling, T.A., eds.), Univ. of North Carolina Press, Chapel Hill, NC, 1969. MR 252100
- [6]
- Kasami, T., The weight enumerators for several classes of subcodes of the {\rm 2}nd order binary Reed-Muller codes, Inform. and Control (Shenyang) \textbf{18 \year 1971}, 369--394. MR 281537
- [7]
- Lachaud, G. and Wolfmann, J., The weights of the orthogonals of the extended quadratic binary Goppa codes, IEEE Trans. Inform. Theory \textbf{36} (1990), 686--692. MR 1053865
- [8]
- MacWilliams, J. and Sloane, N.J.A., The theory of error-correcting codes, North Holland, Amsterdam, 1983.
- [9]
- Melas, C.M., A cyclic code for double error correction, IBM J. Res. Develop. \textbf{4} (1960), 364--366. MR 110594
- [10]
- Oesterl\'e, J., Sur la trace des op\'erateurs de Hecke, Th\`ese de $3^{\roman o}$ cycle, Orsay, 1977.
- [11]
- Schoof, R., Non-singular plane cubic curves over finite fields, J. Combin. Theory Ser. A \textbf{46} (1987), 183--211. MR 914657
- [12]
- Schoof, R. and Van der Vlugt, M., Hecke operators and the weight distributions of certain codes, J. Combin. Theory Ser. A \textbf{57} (1991), 163--186. MR 1111555
- [13]
- Silverman, J., The arithmetic of elliptic curves, Graduate Texts in Math., vol.~106, Springer- Verlag, New York, 1986. MR 817210
- [14]
- Van der Geer, G. and Van der Vlugt, M., Reed-Muller codes and supersingular curves. {\rm I}, Compositio Math. \textbf{84} (1992), 333--367. MR 1189892
- [15]
- Waterhouse, W., Abelian varieties over finite fields, Ann. Sci. \'Ecole Norm. Sup. \textbf{2} (1969), 521--560. MR 265369
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Additional Information:
DOI:
10.1090/S0273-0979-1995-00586-0
PII:
S 0273-0979(1995)00586-0
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