Propelinear structure of Z_{2k}-linear codes

Details Propelinear structure of Z_{2k}-linear codes Propelinear structure of Z_{2k}-linear codes

2009-07-30

arxiv.org/abs/0907.5287v1

Electronic Notes in Discrete Mathematics, Volume 10, November 2001, Pages 100-102

Computer Science

Information Theory

Scientific paper

Let C be an additive subgroup of $\Z_{2k}^n$ for any $k\geq 1$. 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 Gray 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.

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