A code ℤ2ℤ4-additive 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 ℤ2ℤ4-additive codes are studied. Their corresponding binary images, via the Gray map, are ℤ2ℤ 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. In order to do this, the appropriate concept of duality for ℤ2ℤ4-additive codes is defined and the parameters of their dual codes are computed. © 2009 Springer Science+Business Media, LLC.
|Journal||Designs, Codes, and Cryptography|
|Publication status||Published - 1 Feb 2010|
- Binary linear codes
- Quaternary linear codes
- ℤ ℤ -additive codes 2 4
- ℤ ℤ -linear codes 2 4