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New near perfect sequences of even lengths

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Abstract

This paper presents a new method of construction of near perfect sequences of even length N = 2mn where m is an odd prime number and n = (2J + 1), J is an even number. We use a shift sequence associated with a primitive polynomial of degree 2J over a finite field GF(2), together with a pair of completely orthogonal sequences of length m to construct near perfect sequences of odd lengths. We concatenate two near perfect sequences of same odd lengths under certain conditions to obtain new near perfect sequences of even lengths. These near perfect sequences also exist for unbounded lengths over m th roots of unity.

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Acknowledgments

The author expresses her sincere thanks to her supervisor Tom Hall for his valuable contribution to the paper. The author also thanks Sam Blake and Santiago Barrera Acevedo for their help with computer programming.

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  1. School of Mathematical Sciences, Monash University, Clayton, Victoria, Australia

    Rema Hariharan

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  1. Rema Hariharan
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Correspondence to Rema Hariharan.

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Hariharan, R. New near perfect sequences of even lengths. Cryptogr. Commun. 6, 39–46 (2014). https://doi.org/10.1007/s12095-013-0093-y

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  • DOI: https://doi.org/10.1007/s12095-013-0093-y

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