Codes in the projective space over a finite field, referred to as subspace codes, and in particular codes in the Grassmannian, referred to as constant-dimension codes (CDCs), have been proposed for error control in random network coding. In this paper, we first study the covering properties of CDCs. We determine some fundamental geometric properties of the Grassmannian. Using these properties, ...

Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and practice as they have good error-correcting capability and are widely used in communication systems, storage devices and consumer electronics. However, the dimens...

Two sets of points in -dimensional space are given: a data set consisting of points, and a pattern set or probe consisting of points. We address the problem of determining whether there is a transformation, among a specified group of transformations of the space, carrying into or near (meaning at a small directed Hausdorff distance of) . The groups we consider are translations and rigid motions...

We give a complete characterization of receptive field codes realizable by connected receptive fields and their minimal embedding dimensions. In particular, we show that all connected codes are realizable in dimension at most three. To our knowledge, this is the first family of receptive field codes for which the exact characterization and minimal embedding dimension is known.

The effect of lattice mismatch on the chemical ordering of epitaxial FePt films was studied. The results showed that the lattice constant scd of the FePt films decreased with increasing lattice mismatch « from about 2.23% to 6.33%. Upon further increase of « to about 8.8%, c increased. On the other hand, the variation of the lattice constant sad of the FePt films showed a reversal behavior to t...