New sphere packings in dimensions 9-15

Leech, John; Sloane, N. J. A.

doi:10.1090/S0002-9904-1970-12533-2

New sphere packings in dimensions 9-15

Authors: John Leech and N. J. A. Sloane
Journal: Bull. Amer. Math. Soc. 76 (1970), 1006-1010
MSC (1970): Primary 5245
DOI: https://doi.org/10.1090/S0002-9904-1970-12533-2
MathSciNet review: 0266056
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1. John Leech, Notes on sphere packings, Canad. J. Math. 19 (1967), 251–267. MR 0209983, https://doi.org/10.4153/CJM-1967-017-0
2. Marcel J. E. Golay, Binary coding, Trans. I.R.E. PGIT-4 (1954), 23–28. MR 0089123
3. D. Julin, Two improved block codes, IEEE Trans. Information Theory IT-11 (1965), 459.
4. John Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canad. J. Math. 23 (1971), 718–745. MR 0285994, https://doi.org/10.4153/CJM-1971-081-3
5. Neil J. A. Sloane and Donald S. Whitehead, New family of single-error correcting codes, IEEE Trans. Information Theory IT-16 (1970), 717–719. MR 0274195
6. John Leech, Five dimensional non-lattice sphere packings, Canad. Math. Bull. 10 (1967), 387–393. MR 0220170, https://doi.org/10.4153/CMB-1967-037-5
7. John Leech, Six and seven dimensional non-lattice sphere packings, Canad. Math. Bull. 12 (1969), 151–155. MR 0254746, https://doi.org/10.4153/CMB-1969-014-1
8. E. Witt, Über Steinersche Systeme, Abh. Math. Sem. Hansischen Univ. 12 (1938), 256-264.
9. Haim Hanani, On quadruple systems, Canad. J. Math. 12 (1960), 145–157. MR 0111696, https://doi.org/10.4153/CJM-1960-013-3
10. John Leech, Some sphere packings in higher space, Canad. J. Math. 16 (1964), 657–682. MR 0167901, https://doi.org/10.4153/CJM-1964-065-1
11. A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), no. 3, 366–389 (French). MR 1509828, https://doi.org/10.1007/BF01442795
12. T. W. Chaundy, The arithmetic minima of positive quadratic forms. I, Quart. J. Math., Oxford Ser. 17 (1946), 166–192. MR 0017317
13. E. S. Barnes, The construction of perfect and extreme forms. II, Acta Arith. 5 (1959), 205–222. MR 0107635
14. H. S. M. Coxeter and J. A. Todd, An extreme duodenary form, Canadian J. Math. 5 (1953), 384–392. MR 0055381