Results 1  10
of
23
Z2Z4linear codes: generator matrices and duality
, 2007
"... A code C is Z2Z4additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper Z2Z4additive codes are studied. T ..."
Abstract

Cited by 13 (8 self)
 Add to MetaCart
A code C is Z2Z4additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper Z2Z4additive codes are studied. Their corresponding binary images, via the Gray map, are Z2Z4linear 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 Z2Z4additive codes is defined. Moreover, the parameters of the dual codes are computed. Finally, some conditions for selfduality of Z2Z4additive codes are given.
On the additive (Z4linear and nonZ4linear) Hadamard codes. Rank and Kernel
, 2005
"... All the possible nonisomorphic additive (Z4linear and nonZ4linear) Hadamard codes are characterized and, for each one, the rank and the dimension of the kernel is computed. ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
All the possible nonisomorphic additive (Z4linear and nonZ4linear) Hadamard codes are characterized and, for each one, the rank and the dimension of the kernel is computed.
Z2Z4linear codes: rank and kernel
, 2008
"... A code C is Z2Z4additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper, the rank and dimension of the ker ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
A code C is Z2Z4additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper, the rank and dimension of the kernel for Z2Z4linear codes, which are the corresponding binary codes of Z2Z4additive codes, are studied. The possible values of these two parameters for Z2Z4linear codes, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a Z2Z4linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a Z2Z4linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a Z2Z4additive code for each possible pair (r, k) is given.
1Perfect uniform and distance invariant partitions
 APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
, 2001
"... Let F n be the ndimensional vector space over Z2. A (binary) 1perfect partition of F n is a partition of F n into (binary) perfect single errorcorrecting codes or 1perfect codes. We define two metric properties for 1perfect partitions: uniformity and distance invariance. Then we prove the equi ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Let F n be the ndimensional vector space over Z2. A (binary) 1perfect partition of F n is a partition of F n into (binary) perfect single errorcorrecting codes or 1perfect codes. We define two metric properties for 1perfect partitions: uniformity and distance invariance. Then we prove the equivalence between these properties and algebraic properties of the code (the class containing the zero vector). In this way, we characterize 1perfect partitions obtained using 1perfect translation invariant and not translation invariant propelinear codes. The search for examples of 1perfect uniform but not distance invariant partitions enabled us to deduce a nonAbelian propelinear group structure for any Hamming code of length greater than 7.
Perfect Z2Z4linear codes in steganography”, (Available from http://arxiv.org/abs/1002.0026
, 2010
"... Abstract—Product perfect codes have been proven to enhance the performance of the F5 steganographic method, whereas perfect Z2Z4linear codes have been recently introduced as an efficient way to embed data, conforming to the±1steganography. In this paper, we present two steganographic methods. On t ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract—Product perfect codes have been proven to enhance the performance of the F5 steganographic method, whereas perfect Z2Z4linear codes have been recently introduced as an efficient way to embed data, conforming to the±1steganography. 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 Z2Z4linear codes. Finally, the performance of the proposed methods is evaluated and compared with those of the aforementioned schemes. I.
STSGraphs of Perfect Codes Mod Kernel
"... We show that a 1errorcorrecting code C is `foldable' over its kernel via the Steiner triple systems associated to the codewords whenever C is perfect. The resulting `folding' produces a graph invariant that for Vasil'ev codes of length 15 is complete, showing in particular that ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
We show that a 1errorcorrecting code C is `foldable' over its kernel via the Steiner triple systems associated to the codewords whenever C is perfect. The resulting `folding' produces a graph invariant that for Vasil'ev codes of length 15 is complete, showing in particular that there exist nonadditive propelinear codes and just one nonlinear Vasil'ev additive code up to equivalence.