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

Muhammad Ilyas; Mieko Yamada

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

Information Theory 2013-10-22 v1 math.IT

Authors: Muhammad Ilyas , Mieko Yamada

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 $m \geq 3$ .

Cite

@article{arxiv.1310.5225,
  title  = {Generalized Extended Hamming Codes over Galois Ring of Characteristic $2^{n}$},
  author = {Muhammad Ilyas and Mieko Yamada},
  journal= {arXiv preprint arXiv:1310.5225},
  year   = {2013}
}

Comments

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

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