Quaternion Order and Coding Theory

Abstract

We shown the quaternion orders OZ[2] ' ( √ 2,−1)Z[2] and OZ[3] ' (3+2 √ 3,−1)Z[3] that appear in applications of the coding theory [2] are not maximal orders in the quaternion algebras AQ(2) ' ( √ 2,−1)Q(2) and AQ(3) ' (3 + 2 √ 3,−1)Q(3), respectively. Furthermore, we identify the maximal orders that containing these orders. 

Topics

Cite this paper

@inproceedings{Carvalho2012QuaternionOA, title={Quaternion Order and Coding Theory}, author={Edson D. de Carvalho and Antonio Aparecido de Andrade}, year={2012} }