Generalized Extended Hamming Codes over Galois Ring of Characteristic $2^n$

Abstract

In this paper, we introduce generalized extended Hamming codes over Galois rings $GR(2^n,m)$ of characteristic $2^n$ with extension degree $m$. Furthermore we prove that the minimum Hamming weight of generalized extended Hamming codes over $GR(2^n,m)$ is 4 and the minimum Lee weight of generalized extended Hamming codes over $GR(8,m)$ is 6 for all $m\ge 3$.

arXiv comment12 pages, International Symposium on Computational Science 2011 Selected Paper for Gakuto International Series Mathematical Science and Application Volume 34, 2011