15 research outputs found
On the number of nonequivalent propelinear extended perfect codes
The paper proves that there exist an exponential number of nonequivalent
propelinear extended perfect binary codes of length growing to infinity.
Specifically, it is proved that all transitive extended perfect binary codes
found by Potapov are propelinear. All such codes have small rank, which is one
more than the rank of the extended Hamming code of the same length. We
investigate the properties of these codes and show that any of them has a
normalized propelinear representation
Algebraic lattice constellations: bounds on performance
In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain. Furthermore, we discuss constructions, minimum product distance, and bounds for full-diversity complex rotated Z[i]/sup n/-lattices for any dimension n, which avoid the need of component interleaving