  This article presets a review of lattice lattice basis reduction types. Paper
contains the main five types of lattice basis reduction: size reduced (weak
Hermit), c-reduced, Lovasz condition, Hermit-Korkin-Zolotarev, Minkowski
reduced. The article provides references to applications in: information theory
(decoding of coding group in MIMO), calculus (minimize of the positive
quadratic form), complexity theory and cryptanalysis of Merkle-Hellman
cryptography (solving subset sum problems), algebra and control theory(solving
system of linear diophantine equation), compiler theory (lattice based memory
allocation), synthesize cryptographic and cryptanalysis in lattice based
cryptography.
