Matrix Representation of Groups In the Finite Fields GF(p n )
Ahmad Hamza Al Cheikha
1Ahmad Hamza Al Cheikha, Department of Mathematical Science, Ahlia University, Kingdom of Bahrain.
Manuscript received on June 25, 2014. | Revised Manuscript received on July 03, 2014. | Manuscript published on July 05, 2014. | PP: 1-6 | Volume-4, Issue-3, July 2014. | Retrieval Number: C2264074314 /2012©BEIESP
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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(pn), 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.