Self-dual codes over $Z_2timesZ_4$ are subgroups of $Z_2^alpha timesZ_4^beta$ that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible
values $alpha,beta$ such that there exist a code $Csubseteq Z_2^alpha timesZ_4^beta$ are established. Moreover, the construction of a $add$-linear code for each type and possible pair $(alpha,beta)$ is given. Finally, the standard techniques of invariant theory are applied to describe the weight enumerators for each type.
Let C be an additive subgroup of $Z_{2k}^n$ for any $kgeq 1$. We define a Gray map $Phi:Z_{2k}^n longrightarrow Z_2^{kn}$ such that $Phi(codi)$ is a binary propelinear code and, hence, a Hamming-compatible group code. Moreover, $Phi$ is the unique Gr
ay map such that $Phi(C)$ is Hamming-compatible group code. Using this Gray map we discuss about the nonexistence of 1-perfect binary mixed group code.
This paper describes the characterization studies under low magnetic fields of the Hamamatsu R7081 photomultipliers that are being used in the Double Chooz experiment. The design and performances of the magnetic shielding that has been developed for these photomultipliers are also reported.
A code ${cal C}$ is $Z_2Z_4$-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 (respectivel
y, a quaternary linear code). In this paper $Z_2Z_4$-additive codes are studied. Their corresponding binary images, via the Gray map, are $Z_2Z_4$-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 $Z_2Z_4$-additive codes is defined. Moreover, the parameters of the dual codes are computed. Finally, some conditions for self-duality of $Z_2Z_4$-additive codes are given.
