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The merit factor of Legendre sequences (Corresp.)

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1 Author(s)

Turyn has shown by numerical computation that the merit factor of long Legendre sequences offset by a quarter of their length has in all likelihood the asymptotic value 6 . The ergodicity postulate is used in this correspondence to calculate that the merit factor F of a Legendre sequence offset by a fraction f of its length has an asymptotic value given by 1/F=(2/3)-4|f|+8f^{2}, |f|\leq 1/2 , which gives F=6 for |f|=1/4 .

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Information Theory, IEEE Transactions on  (Volume:29 ,  Issue: 6 )