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Leech lattice
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==References== {{Reflist}} *{{Citation | last1=Chapman | first1=Robin | title=Conference matrices and unimodular lattices | doi=10.1006/eujc.2001.0539 | mr=1861046 | zbl=0993.05036 | year=2001 | journal=European Journal of Combinatorics | issn=0195-6698 | volume=22 | issue=8 | pages=1033–1045 | arxiv=math.NT/0007116 | s2cid=744078 }} *{{Citation | last1=Raji | first1=Mehrdad Ahmadzadeh | title=Higher Power Residue Codes and the Leech Lattice | doi=10.1007/s10801-005-6279-4 | year=2005 | journal=Journal of Algebraic Combinatorics | issn=1572-9192 | volume=21 | issue=1 | pages=39–53 | s2cid=120908420 | doi-access=free }} *{{Citation | last1=Cohn | first1=Henry | last2=Kumar | first2=Abhinav | title=Optimality and uniqueness of the Leech lattice among lattices | doi=10.4007/annals.2009.170.1003 | mr=2600869 | zbl=1213.11144 | year=2009 | journal=Annals of Mathematics | issn=1939-8980 | volume=170 | issue=3 | pages=1003–1050 | arxiv=math.MG/0403263 | s2cid=10696627 }} *{{Citation | last1=Cohn | first1=Henry | last2=Kumar | first2=Abhinav | title=The densest lattice in twenty-four dimensions | doi=10.1090/S1079-6762-04-00130-1 | mr=2075897 | year=2004 | journal=Electronic Research Announcements of the American Mathematical Society | issn=1079-6762 | volume=10 | issue=7 | pages=58–67 |arxiv=math.MG/0408174 | bibcode=2004math......8174C | s2cid=15874595 }} *{{citation|title=The sphere packing problem in dimension 24| journal=Annals of Mathematics| volume=185| issue=3| pages=1017–1033| first1=Henry|last1= Cohn|first2= Abhinav|last2= Kumar|first3= Stephen D. |last3=Miller|first4= Danylo |last4=Radchenko|first5= Maryna |last5=Viazovska|authorlink5=Maryna Viazovska|year=2017|arxiv=1603.06518|bibcode=2016arXiv160306518C| doi=10.4007/annals.2017.185.3.8| s2cid=119281758}} *{{Citation | last1=Conway | first1=John Horton | author1-link=John Horton Conway | title=A perfect group of order 8,315,553,613,086,720,000 and the sporadic simple groups | mr=0237634 | year=1968 | journal=[[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the United States of America]] | volume=61 | pages=398–400 | doi=10.1073/pnas.61.2.398 | pmid=16591697 | issue=2| pmc=225171 | bibcode=1968PNAS...61..398C | doi-access=free }} *{{Citation | last1=Conway | first1=John Horton | author1-link=John Horton Conway | title=The automorphism group of the 26-dimensional even unimodular Lorentzian lattice | doi=10.1016/0021-8693(83)90025-X | mr=690711 | year=1983 | journal=[[Journal of Algebra]] | issn=0021-8693 | volume=80 | issue=1 | pages=159–163| doi-access=free }} *{{Citation | last1=Conway | first1=John Horton | author1-link=John Horton Conway | last2=Sloane | first2=N. 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A. | author2-link=Neil Sloane | title=Twenty-three constructions for the Leech lattice | doi=10.1098/rspa.1982.0071 | mr=661720 | year=1982 | journal=[[Proceedings of the Royal Society A]] | issn=0080-4630 | volume=381 | issue=1781 | pages=275–283| bibcode=1982RSPSA.381..275C | s2cid=202575295 }} *{{citation | zbl=0915.52003 | last1=Conway | first1=J.H. | author1-link=John Horton Conway | last2=Sloane | first2=N.J.A. | author2-link=Neil Sloane | others=With contributions by Bannai, E.; Borcherds, R. E.; Leech, J.; Norton, S. P.; Odlyzko, A. M.; Parker, R.A.; Queen, L.; Venkov, B.B. | title=Sphere packings, lattices and groups | edition=Third | series=Grundlehren der Mathematischen Wissenschaften | volume=290 | location=New York, NY | publisher=[[Springer-Verlag]] | isbn=978-0-387-98585-5 | mr=662447 | year=1999 | url-access=registration | url=https://archive.org/details/spherepackingsla0000conw_b8u0 }} *{{citation | first=Marcus| last=Du Sautoy | title=Finding Moonshine | isbn=978-0-00-721462-4 | publisher=Fourth Estate| year=2009 }} *{{citation | last=Griess | first=Robert L. | title=Twelve Sporadic Groups | publisher=Springer-Verlag | year=1998 | series=Springer Monographs in Mathematics | location=Berlin | isbn=978-3-540-62778-4 | doi=10.1007/978-3-662-03516-0 | mr=1707296}} *{{Citation | last1=Leech | first1=John | title=Some sphere packings in higher space | doi=10.4153/CJM-1964-065-1 | mr=0167901 | year=1964 | journal=[[Canadian Journal of Mathematics]] | issn=0008-414X | volume=16 | pages=657–682| s2cid=123244939 | doi-access=free }} *{{Citation | last1=Leech | first1=John | title=Notes on sphere packings | doi=10.4153/CJM-1967-017-0 | mr=0209983 | year=1967 | journal=[[Canadian Journal of Mathematics]] | issn=0008-414X | volume=19 | pages=251–267| doi-access=free }} *{{Citation | last1=O'Connor | first1=R. E. | last2=Pall | first2=G. | title=The construction of integral quadratic forms of determinant 1 | doi=10.1215/S0012-7094-44-01127-0 | mr=0010153 | year=1944 | journal=[[Duke Mathematical Journal]] | issn=0012-7094 | volume=11 | issue=2 | pages=319–331}} *{{citation | last=Thompson | first=Thomas M | title=From Error Correcting Codes through Sphere Packings to Simple Groups | series=Carus Mathematical Monographs | publisher=Mathematical Association of America | year=1983 | mr=0749038 | volume=21 | location=Washington, DC | isbn=978-0-88385-023-7}} *{{citation | last=Ronan | first=Mark | title=Symmetry and the Monster | publisher=Oxford University Press| isbn=978-0-19-280722-9 | location=Oxford | year=2006 | mr=2215662}} *{{Citation | last1=Wilson | first1=Robert A. | title=Octonions and the Leech lattice | mr=2542837 | year=2009 | journal=Journal of Algebra | volume=322 | issue=6 | pages=2186–2190| doi=10.1016/j.jalgebra.2009.03.021 | doi-access=free }} *{{Citation | last1=Witt | first1=Ernst | author1-link=Ernst Witt | title=Eine Identität zwischen Modulformen zweiten Grades | doi=10.1007/BF02940750 | mr=0005508 | year=1941 | journal=Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg | volume=14 | pages=323–337| s2cid=120849019 }} *{{Citation | last1=Witt | first1=Ernst | author1-link=Ernst Witt | title=Collected papers. Gesammelte Abhandlungen | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-57061-5 | mr=1643949 | year=1998}}
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