Energy bounds for codes and designs in Hamming spaces

The Covering Problem in Rosenbloom-Tsfasman Spaces

We investigate the covering problem in RT spaces induced by the RosenbloomTsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen an...

On the roots and minimum rank distance of skew cyclic codes

Skew cyclic codes play the same role as cyclic codes in the theory of errorcorrecting codes for the rank metric. In this paper, we give descriptions of these codes by idempotent generators, root spaces and cyclotomic spaces. We prove that the lattice of skew cyclic codes is anti-isomorphic to the lattice of root spaces and extend the rank-BCH bound on their minimum rank distance to rank-metric ...

Improved bounds on identifying codes in binary Hamming spaces

Title of dissertation : BOUNDS ON THE SIZE OF CODES

Title of dissertation: BOUNDS ON THE SIZE OF CODES Punarbasu Purkayastha Doctor of Philosophy, 2010 Dissertation directed by: Professor Alexander Barg Department of Electrical and Computer Engineering and The Institute for Systems Research In this dissertation we determine new bounds and properties of codes in three different finite metric spaces, namely the ordered Hamming space, the binary Ha...

Lower bounds for designs in symmetric spaces

A design is a finite set of points in a space on which every ”simple” functions averages to its global mean. Illustrative examples of simple functions are low-degree polynomials on the Euclidean sphere or on the Hamming cube. We prove lower bounds on designs in spaces with a large group of symmetries. These spaces include globally symmetric Riemannian spaces (of any rank) and commutative associ...