The Covering Problem in Rosenbloom-Tsfasman Spaces

We investigate the covering problem in RT spaces induced by the Rosenbloom-Tsfasman 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 and Honkala, Brualdi et al., Yildiz et al. A new construction of MDS codes in RT spaces is obtained. Upper bounds are given on the basis of MDS codes, generalizing well-known results due to Stanton et al., Blokhuis and Lam, and Carnielli. Tables of lower and upper bounds are presented too.

A High-Capacity Covering Code for Voice-Over-IP Steganography

Although steganographic transparency and embedding capacity are considered to be two conflicting objectives in the design of steganographic systems, it is possible and necessary to strike a good balance between them in Voice-over-IP steganography. In this paper, to improve steganographic transparency while maintaining relatively large embedding capacity, the authors present a (2n-1, 2n) covering code, which can hide 2n-1 bits of secret messages into 2n bits of cover messages with not more than n-bit changed. Specifically, each (2n-1)-bit secret message is first transformed into two 2n-bit candidate codewords. In embedding process, the cover message is replaced with the optimal codeword more similar with it. In this way, the embedding distortion can be largely reduced. The proposed method is evaluated by comparing with existing ones with a large number of ITU-T G.729a encoded speech samples. The experimental results show that the authors' scheme can provide good performance on both steganographic transparency and embedding capacity, and achieve better balance between the two objectives than the existing ones.

Lower Bounds for the Football Pool Problem for 7 and 8 Matches

Let $k_3(n)$ denote the minimal cardinality of a ternary code of length $n$ and covering radius one. In this paper we show $k_3(7)\ge 156$ and $k_3(8)\ge 402$ improving on the best previously known bounds $k_3(7)\ge 153$ and $k_3(8)\ge 398$. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities satisfied by the number of elements of a covering code, that lie in $k$-dimensional subspaces of F${}_3^n$.