Codes and lattices are very important subjects in combinatorics. They have many applications in telecommunication, design theory, finite group theory as well as many different fields in electronic
engineering and physics.

In this thesis, we will give a survey on the construction of lattices by using some linear codes. In particular, we will concentrate on the construction of certain even unimodular lattices by using binary and ternary codes. We will also compare various methods.

[1] P. S. Montague,“A new constructions of lattices from codes over GF(3)”, Discrete Math. 135,193--223,1994.
[2] J. H. Conway, N. J. A. Sloane,“Sphere Packings, Lattices and Groups”, Springer, 1999.
[3] F. J. MacWilliams, N. J. A. Sloane,“The Theory of Error-Correcting Codes”, North-Holland Pub. Co., Amsterdam, 1977.
[4] W. Ebeling,“Lattices and Codes”, Vieweg, 2002.
[5] H. Samelson,“Notes on Lie Algebras”, Springer-Verlag, New York, 1990.
[6] James E. Humphreys,“Reflection groups and coxeter groups”, Cambridge University Press,New York,1990.
[7] Masaaki Harada and Masaaki Kitazume,“Z4-Code constructions for the Niemeier Lattices and their Embeddings in the Leech Lattice ”, Europ.J.Combinatorics(2000)21.
[8] A. Bonnecaze, P. Sole, A.R. Calderbank,“Quaternary Quadratic Residue Codes and Unimodular Lattices”, IEEE Trans. Inform. Theory 43, 969--976, 1997.
[9] H.-V. Niemeier,“Definete quadraticische Formen der Dimension 24 and Diskriminate 1 ”, J.Number Theory 5(1973)142--178.
[10] N. Bourbaki,“Groups et Algebras de Lie”, Chapitres 4, 5 et 6, Hermann, Paris,1968.
[11] Mehrdad Ahmadzadeh Raji,“Higher Power Residue Codes and the Leech Lattices ”, Journal of Algebraic Combinatorics, 21,39--53,2005.
[12] M. Harada, M. Kitazume,“Z6-Code Constructions of the Leech Lattices and the Niemeier Lattices ”, Europ. J. Combinatorics 23, 573--581, 2002.
[13] J, Leech,“Notes on sphere packings”, Can. J. Math. 19,251--267,1967.
[14] H.V. Niemeier,“Definite quadratische Formen der Dimension 24 und Diskriminate 1”, J.Number Theory 5, 142--178,1973.
[15] J.H. Conway, R.A. Parker, and N.J.A. Sloane,“On the enumeration of lattices of determine one”, J.Number Theory,1982.
[16] B.B. Venkov,“On the classification of integral even unimodular 24-dimensional quadratic forms”, Proc.Steklov Inst. Math.issue 4, pp.63--74,1980.
[17] J.H. Conway,“Three lectures on exceptional groups”, In Finite simple groups (ed.M.B.Powell and G.Higman),pp.215--247,1971.Newo York: Academic Press.
[18] M. Craig,“A cyclotomic construction for Leech's lattice”, Mathematika, 25 236--241,1978.
[19] J. Leech, and N.J.A. Sloane,“Sphere packings and error-correcting codes”, Can.J.Math.23, 718--745,1971.
[20] J.I. Lepowsky, and A.E. Meurman,“An E8-approch to the Leech lattice and the Conway group”, Preprint,1982.
[21] J.H. Lindsey,II,“On the Suzuki and Conway groups”. In Representation theory of finite groups and related topics (Proc.Symp.Pure Math.,vol.XXI,pp.107--109.
Providence, Rhode Island: American Mathematical Society),1971.
[22] J.H. Lindsey,II,“A correlation between PSU4(3),
the Suzuki group, and the Conway group”, Trans.Am.math. Soc.157 189--204,1971.
[23] J. McKay,“A setting for the Leech lattice ”. In Finite groups '72 (ed.T.Gagen et al.), pp.117--118.Amsterdam:North-Holland,1973.
[24] J. Tits,“Four presentations of Leech's lattice ”. In Finite simple groupsII (ed M.J.Collins), pp 303--307, 1980. New York: Academic Press.
[25] J. Tits,“Quaternions over Q[sqrt{5}], Leech's lattice and thesporadic group of Hall-Janko”,J.Algebra,63,56--75,1980.
[26] J.H. Conway,“A characterisation of Leech's lattice”, Invent.Math. 7,17--142,1969.
[27] Masaaki. Harada,“Type II codes over Z2k and the Leech lattice”.In Codes, lattices, vertex operator algebras and finite groups (Japanse) (Kyoto,2001),35--42.