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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2019, Volume & Issue : BPAS-Maths & Stat 38E(1), JAN-JUN 2019
Page No. : 155-158, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2019.00013.4 (Received on 04.12.2018, Revised on 19.02.2019 Accepted on 20.03.2019)

SYMMETRY GROUPS OF SOME HADAMARD MATRICES

N.V. Ramana Murty1,*, G.M. Victor Emmanuel2, P. Venu Gopala Rao3, M. Maria Das4
Author’s Affiliation : 1Department of Mathematics, Andhra Loyola College, Vijayawada, Andhra Pradesh 520008, India E-mail: [email protected] 2Department of Mathematics, Andhra Loyola College, Vijayawada, Andhra Pradesh 520008, India E-mail: [email protected] 3Department of Mathematics, Andhra Loyola College, Vijayawada, Andhra Pradesh 520008, India E-mail: [email protected] 4Department of Mathematics, Andhra Loyola College, Vijayawada, Andhra Pradesh 520008, India E-mail: [email protected]

Corresponding Author : N.V. Ramana Murty, Department of Mathematics, Andhra Loyola College, Vijayawada, Andhra Pradesh 520008, India ,
E-Mail:-[email protected]


Abstract

Hadamard matrices are a special class of square matrices with entries 1 and -1 only. They have many applications in Coding Theory, Physics, Chemistry and Neural networks. Therefore, this paper makes an attempt to study Hadamard matrices and their connection with Group Theory. Especially, we concentrate on the Symmetry groups of Standard Hadamard matrices  and  It is shown that the Symmetry group of the Standard Hadamard matrices  and  is the trivial group and that of  is isomorphic to the Permutation group Since Symmetry group of the Standard Hadamard matrix  is isomorphic to the General linear group of  invertible matrices over the field  and the order of the General linear group  of  invertible matrices over a finite field  containing  elements is , it is shown that the orders of the Symmetry groups of  and  are 168 and 20,160 respectively.

Keywords

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