Good Random Matrices over Finite Fields

The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is uniformly distributed over a maximum-rank-distance (MRD) code of minimum rank distance min{m,n}-k+1, and vice versa. Further examples of k-good random matrices are derived from homogeneous weights on matrix modules. Several applications of k-good random matrices are given, establishing links with some well-known combinatorial problems. Finally, the related combinatorial concept of a k-dense set of m-by-n matrices is studied, identifying such sets as blocking sets with respect to (m-k)-dimensional flats in a certain m-by-n matrix geometry and determining their minimum size in special cases.Comment: 25 pages, publishe

Z2Z4-Additive Perdect Codes in Steganography

Steganography is an information hiding application which aims to hide secret data imperceptibly into a cover object. In this paper, we describe a novel coding method based on Z2Z4-additive codes in which data is embedded by distorting each cover symbol by one unit at most (+-1-steganography). This method is optimal and solves the problem encountered by the most e cient methods known today, concerning the treatment of boundary values. The performance of this new technique is compared with that of the mentioned methods and with the well-known rate-distortion upper bound to conclude that a higher payload can be obtained for a given distortion by using the proposed method

Characterization results on weighted minihypers and on linear codes meeting the G(r)iesmer bound

A