A code C is said to be Z2Z4-additive if its coordinates can be partitioned into two subsets X and Y , in such a way that the punctured code of C obtained by removing the coordinates outside X (or, respectively, Y ) is a binary linear code (respectively, a quaternary linear code). The binary image of a Z2Z4-additive code, through the Gray map, is a Z2Z4-linear code, which is not always linear. G...

Let C be an additive subgroup of Z n 2k for any k ≥ 1. We define a Gray map Φ : Z n 2k −→ Z kn 2 such that Φ(C) 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.

Brualdi et al. introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Hamming code to be a double-error-correcting perfect P-code. Our study is motivated by this example. In this paper we classify all poset structures which admit the extended binary Hamming code to be a double or triple-error-correcting perfect P-code. © 2004 Elsevier B.V....