Shift-inequivalent decimations of the Sidelnikov–Lempel–Cohn–Eastman sequences
نویسندگان
چکیده
منابع مشابه
On Decimations of -Sequences∗
Maximal length Feedback with Carry Shift Register sequences have several remarkable statistical properties. Among them is the property that the arithmetic correlations between any two cyclically distinct decimations are precisely zero. It is open, however, whether all such pairs of decimations are indeed cyclically distinct. In this paper we show that the set of distinct decimations is large an...
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Let a be an l-sequence generated by a feedback-with-carry shift register with connection integer q = pe, where p is an odd prime and e 1. Goresky and Klapper conjectured that when pe = 2 f5; 9; 11; 13g, all decimations of a are cyclically distinct. When e = 1 and p > 13, they showed that the set of distinct decimations is large and, in some cases, all deciamtions are distinct. In this article, ...
متن کاملDECIMATIONS OF -SEQUENCES AND PERMUTATIONS OF EVEN RESIDUES mod p∗
Goresky and Klapper conjectured that for any prime p > 13 and any -sequence a based on p, every pair of allowable decimations of a is cyclically distinct. The conjecture is essentially equivalent to the statement that the mapping x → Axd, with (d, p− 1) = 1, p A, is a permutation of the even residues (mod p) if and only if d = 1 and A ≡ 1 (mod p) for p > 13. We prove the conjecture for p > 2.26...
متن کاملAutocorrelation and Distinctness of Decimations of l-Sequences
It has long been open whether all pairs of proper decimations of l-sequences based on primes are cyclically distinct. By determining the nontrivial maximal autocorrelation of l-sequences, this paper presents a partial proof of the distinctness problem. Since the proof idea is completely different from former ones, the set of decimations that are known to be cyclically distinct is further enlarg...
متن کاملProof of the Goresky Klapper Conjecture on Decimations of L-sequences
Let p be an odd prime and E = {2, 4, . . . , p−1} the set of nonzero even residues in Zp = Z/(p). We prove that for p > 13, if the mapping x → Axk is a permutation of Zp, but not the identity mapping, then the mapping is not a permutation of E. This establishes a conjecture of Goresky and Klapper stating that any two distinct decimations of a binary `-sequence are cyclically distinct.
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2019
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-019-00697-8