Integer codes and lattice packings by cubes of sidelength k

2015 ◽  
Author(s):  
Ulrich Tamm
Keyword(s):  
Integer Codes ◽  
Lattice Packings

Soft Decoding of Integer Codes and Their Application to Coded Modulation

2010 ◽  
Vol E93-A (7) ◽  
pp. 1363-1370 ◽  
Author(s):  
Hristo KOSTADINOV ◽  
Hiroyoshi MORITA ◽  
Noboru IIJIMA ◽  
A. J. HAN VINCK ◽  
Nikolai MANEV
Keyword(s):  
Coded Modulation ◽  
Soft Decoding ◽  
Integer Codes

Some Sphere Packings in Higher Space

1964 ◽  
Vol 16 ◽  
pp. 657-682 ◽  
Author(s):  
John Leech
Keyword(s):  
Two Dimensions ◽  
Lattice Packing ◽  
Sphere Packings ◽  
Euclidean Spaces ◽  
Lattice Packings

This paper is concerned with the packing of equal spheres in Euclidean spaces [n] of n > 8 dimensions. To be precise, a packing is a distribution of spheres any two of which have at most a point of contact in common. If the centres of the spheres form a lattice, the packing is said to be a lattice packing. The densest lattice packings are known for spaces of up to eight dimensions (1, 2), but not for any space of more than eight dimensions. Further, although non-lattice packings are known in [3] and [5] which have the same density as the densest lattice packings, none is known which has greater density than the densest lattice packings in any space of up to eight dimensions, neither, for any space of more than two dimensions, has it been shown that they do not exist.

scholarly journals Integer codes correcting burst asymmetric within a byte and double asymmetric errors

2019 ◽  
Vol 12 (2) ◽  
pp. 221-230
Author(s):  
Aleksandar Radonjic ◽  
Vladimir Vujicic
Keyword(s):  
Asymmetric Errors ◽  
Integer Codes

scholarly journals A NEW INEQUALITY FOR THE HERMITE CONSTANTS

2008 ◽  
Vol 04 (03) ◽  
pp. 363-386
Author(s):  
ROLAND BACHER
Keyword(s):  
Dimensional Lattice ◽  
Maximal Density ◽  
Hermite’S Constant ◽  
Increasing Functions ◽  
Lattice Packings

We describe continuous increasing functions Cn(x) such that γn ≥ Cn(γn-1) where γm is Hermite's constant in dimension m. This inequality yields a new proof of the Minkowski–Hlawka bound Δn ≥ ζ(n)21-n for the maximal density Δn of n-dimensional lattice packings.

Finite Lattice Packings and the Wulff‐Shape

Mathematika ◽  
2005 ◽  
Vol 52 (1-2) ◽  
pp. 17-29
Author(s):  
Ulrich Betke ◽  
Károly Böröczky
Keyword(s):  
Finite Lattice ◽  
Wulff Shape ◽  
Lattice Packings

Integer codes correcting double asymmetric errors

2016 ◽  
Vol 10 (14) ◽  
pp. 1691-1696 ◽  
Author(s):  
Aleksandar Radonjic ◽  
Karlo Bala ◽  
Vladimir Vujicic
Keyword(s):  
Asymmetric Errors ◽  
Integer Codes
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