arXiv subjects

J. Rifa

Publications and source records attributed to J. Rifa.

5 recordsLinked to original sources

arXiv2013

On a family of binary completely transitive codes with growing covering radius

A new family of binary linear completely transitive (and, therefore, completely regular) codes is constructed. The covering radius of these codes is growing with the length of the code. In particular, for any integer r > 1, there exist two codes with d=3, covering radius r and length 2r(4r-1) and (2r+1)(4r+1), respectively. These new completely transitive codes induce, as coset graphs, a family of distance-transitive graphs of growing diameter.

cs.IT↗

arXiv2010

Product Perfect Z2Z4-linear codes in Steganography

Product perfect codes have been proven to enhance the performance of the F5 steganographic method, whereas perfect Z2Z4-linear codes have been recently introduced as an efficient way to embed data, conforming to the +/-1-steganography. In this paper, we present two steganographic methods. On the one hand, a generalization of product perfect codes is made. On the other hand, this generalization is applied to perfect Z2Z4-linear codes. Finally, the performance of the proposed methods is evaluated and compared with those of the aforementioned schemes.

cs.IT↗

arXiv2009

Propelinear structure of Z_{2k}-linear codes

Let C be an additive subgroup of $\Z_{2k}^n$ for any $k\geq 1$. We define a Gray map $Φ:\Z_{2k}^n \longrightarrow \Z_2^{kn}$ such that $Φ(\codi)$ is a binary propelinear code and, hence, a Hamming-compatible group code. Moreover, $Φ$ is the unique Gray map such that $Φ(C)$ is Hamming-compatible group code. Using this Gray map we discuss about the nonexistence of 1-perfect binary mixed group code.

cs.IT↗

arXiv2008

New completely regular q-ary codes based on Kronecker products

For any integer $ρ\geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $ρ$ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius $ρ$, which are not completely regular, is also given. In both constructions the Kronecker product is the basic tool that has been used.

cs.IT↗

arXiv2007

Z2Z4-linear codes: generator matrices and duality

A code ${\cal C}$ is $\Z_2\Z_4$-additive if the set of coordinates can be partitioned into two subsets $X$ and $Y$ such that the punctured code of ${\cal C}$ by deleting the coordinates outside $X$ (respectively, $Y$) is a binary linear code (respectively, a quaternary linear code). In this paper $\Z_2\Z_4$-additive codes are studied. Their corresponding binary images, via the Gray map, are $\Z_2\Z_4$-linear codes, which seem to be a very distinguished class of binary group codes. As for binary and quaternary linear codes, for these codes the fundamental parameters are found and standard forms for generator and parity check matrices are given. For this, the appropriate inner product is deduced and the concept of duality for $\Z_2\Z_4$-additive codes is defined. Moreover, the parameters of the dual codes are computed. Finally, some conditions for self-duality of $\Z_2\Z_4$-additive codes are given.

cs.IT↗