Even lattices and doubly even codes

Masaaki KITAZUME; Takeshi KONDO; Izumi MIYAMOTO

doi:10.2969/jmsj/04310067

Masaaki KITAZUME, Takeshi KONDO, Izumi MIYAMOTO

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ジャーナルフリー

1991 年 43 巻 1 号 p. 67-87

DOI https://doi.org/10.2969/jmsj/04310067

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Published: 1991 Received: 1989/04/25 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) M. Broué, Codes correcteurs d'erreurs auto-orthogonaux sur le corps a deux elements et formes quadratiques entieres definies positives a discriminant +1, Discrete Math., 17 (1977), 247-269.
2) M. Broué and M. Enguehard, Une famille infinie de formes quadratiques entieres; leur groupes d'automorphismes, Ann. Sci. École Norm. Sup., 6 (1973), 17-52.
3) J. H. Conway, A characterisation of Leech's lattice, Invent. Math., 7 (1969),137-142.
4) J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Grundleh-ren Math. Wiss., 290, Springer, 1988.
5) J. H. Conway and Vera Pless, On the enumeration of self-dual codes, J. Combin. Theory Ser. A, 28 (1980), 26-53.
6) M. Ozeki, Examples of even unimodular extremal lattices of rank 40 and their Siegel theta-series of degree 2, J. Number Theory, 28 (1988), 119-131.
7) M. Ozeki, On the relation between the invariants of a doubly even self-dual code C and the invariants of the even unimodular lattice L(C) defined from the code C, Research Institute for Mathematical Sciences, Kyoto Univ. RIMS Kokyuroku, 1988, pp. 126-138.
8) Vera Pless, On the uniqueness of the Golay codes, J. Combin. Theory, 5 (1968), 215-228.
9) Vera Pless and N. J. A. Sloane, On the classification and enumeration of self-dual codes, J. Combin. Theory, Ser. A, 18 (1975), 313-335.
10) N. J. A. Sloane, Self-dual codes and lattices, Proc. Sympos. Pure Math., 34 (1979), 273-308.
11) T. Tasaka, On even lattices of 2-square type and self-dual codes, J. Fac. Sci. Univ. Tokyo Sect. IA., 28 (1982), 701-714.

Right : [1] M. Broué, Codes correcteurs d'erreurs auto-orthogonaux sur le corps a deux elements et formes quadratiques entieres definies positives a discriminant +1, Discrete Math., 17 (1977), 247-269.
[2] M. Broué and M. Enguehard, Une famille infinie de formes quadratiques entieres; leur groupes d'automorphismes, Ann. Sci. École Norm. Sup., 6 (1973), 17-52.
[3] J. H. Conway, A characterisation of Leech's lattice, Invent. Math., 7 (1969), 137-142.
[4] J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Grundlehren Math. Wiss., 290, Springer, 1988.
[5] J. H. Conway and Vera Pless, On the enumeration of self-dual codes, J. Combin. Theory Ser. A, 28 (1980), 26-53.
[6] M. Ozeki, Examples of even unimodular extremal lattices of rank 40 and their Siegel theta-series of degree 2, J. Number Theory, 28 (1988), 119-131.
[7] M. Ozeki, On the relation between the invariants of a doubly even self-dual code C and the invariants of the even unimodular lattice L (C) defined from the code C, Research Institute for Mathematical Sciences, Kyoto Univ. RIMS Kokyuroku, 1988, pp. 126-138.
[8] Vera Pless, On the uniqueness of the Golay codes, J. Combin. Theory, 5 (1968), 215-228.
[9] Vera Pless and N. J. A. Sloane, On the classification and enumeration of self-dual codes, J. Combin. Theory, Ser. A, 18 (1975), 313-335.
[10] N. J. A. Sloane, Self-dual codes and lattices, Proc. Sympos. Pure Math., 34 (1979), 273-308.
[11] T. Tasaka, On even lattices of 2-square type and self-dual codes, J. Fac. Sci. Univ. Tokyo Sect. IA., 28 (1982), 701-714.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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