Characterization of m-Sequences of Lengths $2^{2k}-1$ and $2^k-1$ with Three-Valued Crosscorrelation
نویسندگان
چکیده
Considered is the distribution of the crosscorrelation between m-sequences of length 2−1, where m = 2k, and m-sequences of shorter length 2 − 1. New pairs of m-sequences with three-valued crosscorrelation are found and the complete correlation distribution is determined. Finally, we conjecture that there are no more cases with a three-valued crosscorrelation apart from the ones proven here.
منابع مشابه
F eb 2 00 7 Characterization of m - Sequences of Lengths 2 2 k − 1 and 2 k − 1 with Three - Valued Crosscorrelation
Considered is the distribution of the crosscorrelation between m-sequences of length 2−1, where m = 2k, and m-sequences of shorter length 2 − 1. New pairs of m-sequences with three-valued crosscorrelation are found and the complete correlation distribution is determined. Finally, we conjecture that there are no more cases with a three-valued crosscorrelation apart from the ones proven here.
متن کاملBinary m-sequences with three-valued crosscorrelation: A proof of Welch's conjecture
We prove the long-standing conjecture of Welch stating that for odd = 2 + 1, the power function with = 2 + 3 is maximally nonlinear on GF (2 ) or, in other terms, that the crosscorrelation function between a binary maximum-length linear shift register sequences of degree and a decimation of that sequence by 2 + 3 takes on precisely the three values 1 1 2 .
متن کاملar X iv : c s / 06 08 12 3 v 1 [ cs . I T ] 3 1 A ug 2 00 6 Proof of a Conjecture of Helleseth Regarding Pairs of Binary m - Sequences ∗
–Binary m-sequences are maximal length sequences generated by shift registers of length m, that are employed in navigation, radar, and spread-spectrum communication. It is well known that given a pair of distinct m-sequences, the crosscorrelation function must take on at least three values. This correspondence shows the three correlation values are symmetric about -1. The main result is a proof...
متن کاملLong Minimal Zero - Sum Sequences in the Group C
A sequence in an additively written abelian group is called a minimal zero-sum sequence if its sum is the zero element of the group and none of its proper subsequences has sum zero. The structure of the longest minimal zero-sum sequences in the group C2 ⊕C2k is known. Their length is equal to 2k + 1. We characterize the minimal zero-sum sequences in C2 ⊕ C2k (k ≥ 3) with lengths at least 2�k/2�...
متن کاملNew Family of Binary Sequences with Four-valued Cross-correlation
In this paper, we find the values and the number of occurrences of each value of the cross-correlation function Cd(τ) when d = 2k−1 2s−1 (2 k(i+1) − 2ki + 2s+1 − 2k − 1), where n = 2k, s is an integer such that 2s divides k, and i is odd.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IEEE Trans. Information Theory
دوره 53 شماره
صفحات -
تاریخ انتشار 2007