Matrix Representation of Groups in the Finite Fields GF (2 n)
Ahmad Hamza Al Cheikha
Ahmad Hamza Al Cheikha, Department of Mathematical Science, Ahlia University, Kingdom of Bahrain.
Manuscript received on May 01, 2014. | Revised Manuscript received on May 05, 2014. | Manuscript published on May 05, 2014. | PP: 118-125 | Volume-4 Issue-2, May 2014. | Retrieval Number: B2227054214/2014©BEIESP
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©The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: The representation of mathematical fields can be accomplished by binary rows (or columns) of a binary triangular matrix as the Hamming’s matrices, but this representation don’t show the basic product properties of the fields, that is the nonzero elements of the fields forms a cyclic multiplicative group. In this paper we show that the elements of the fields GF(2n ), and their subgroups, can represent as square matrices by m – sequences, which satisfies the product properties as a cyclic group.
Keywords: Galois fields, m-sequences, cyclic groups, Orthogonal sequences.