Volume : II, Issue : X, October - 2013

An Alternative Method to Construct Turyn Type Sequences of Length 34

A. A. C. A. Jayathilake, A. A. I. Perera, M. A. P. Chamikara

Abstract :

The Hadamard conjecture is that Hadamard matrices exist for all orders 1,2,4t where t≥1 is an integer. The most compatible way of constructing Hadamard matrices is to use the Kronecker product whenever there exist a Hadamard matrix of order t above. Otherwise, the most convenient way to develop a Hadamard matrix is to use certain sequences of zeros and ones both positive and negative. In this research, the focus is to discuss an alternative method to construct a set of sequences of ones, both positive and negative called Turyn type sequences which can be used to form a set of sequences with zeros and ones such as Base sequences and T–sequences, which are useful in constructing certain Hadamard matrices. Turyn type sequences,TT(n) are quadruples of {±1}sequences,(A,B,C,D) of length n,n,n,n–1 respectively,where the sum of non–periodic auto–correlation function of A,B and twice that of C,D vanishes everywhere except at zero.The proposed procedure consists of segmentation algorithms of constructing TT(34) that consist of three sequences of length 34 and a sequence of length 33 together with an algorithm to verify the non–periodic auto–correlation condition and the properties of Turyn type sequences. These algorithms are created treating each sequence as a binary number and try all the possible sets of sequences that satisfy the non–periodic auto–correlation condition. Thereupon, by checking the properties of the Turyn type sequences using C/C++ computer program will lead to the desired set of sequences.

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Article: Download PDF   DOI : 10.36106/ijsr  

Cite This Article:

A.A.C.A.Jayathilake, A.A.I.Perera, M.A.P.Chamikara / An Alternative Method to Construct Turyn Type Sequences of Length 34 / International Journal of Scientific Research, Vol.2, Issue.10 October 2013

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