منابع مشابه
Around Pelikán’s conjecture on very odd sequences
Very odd sequences were introduced in 1973 by Pelikán who conjectured that there were none of length ≥ 5. This conjecture was disproved first by MacWilliams and Odlyzko [17] in 1977 and then by two different sets of authors in 1992 [1], 1995 [9]. We give connections with duadic codes, cyclic difference sets, levels (Stufen) of cyclotomic fields, and derive some new asymptotic results on the len...
متن کاملA Generalization of Very Odd Sequences
Let N be the set of positive integers and n ∈ N. Let a = (a0, a1, . . . , an−1) be a sequence of length n, with ai ∈ {0, 1}. For 0 6 k 6 n− 1, let Ak(a) = ∑ 06i6j6n−1 j−i=k aiaj . The sequence a is called a very odd sequence if Ak(a) is odd for all 0 6 k 6 n − 1. In this paper, we study a generalization of very odd sequences and give a characterisation of these sequences.
متن کاملBarker sequences of odd length
A Barker sequence is a binary sequence for which all non-trivial aperiodic autocorrelations are at most 1 in magnitude. An old conjecture due to Turyn asserts that there is no Barker sequence of length greater than 13. In 1961, Turyn and Storer gave an elementary, though somewhat complicated, proof that this conjecture holds for odd lengths. We give a new and simpler proof of this result.
متن کاملCross-Correlations of Quadratic Form Sequences in Odd Characteristic
Cross-correlation functions are determined for a large class of geometric sequences based on m-sequences in odd characteristic. These sequences are shown to have low cross-correlation values in certain cases. They also have significantly higher linear spans than previously studied geometric sequences. These results show that geometric sequences are candidates for use in spread-spectrum communic...
متن کاملRun Vector Analysis and Barker Sequences of Odd Length
The run vector of a binary sequence reflects the run structure of the sequence, which is given by the set of all substrings of the run length encoding. The run vector and the aperiodic autocorrelations of a binary sequence are strongly related. In this paper, we analyze the run vector of skew-symmetric binary sequences. Using the derived results we present a new and different proof that there e...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1995
ISSN: 0097-3165
DOI: 10.1016/0097-3165(95)90017-9