S. W. Golomb and G. Gong, Periodic binary sequences with the "Trinomial Property",IEEE Trans. on Inform. Theory, vol. 45, No. 4, May 1999, pp. 1276-1279. Home/Search Document Not in Database Summary Related Articles Check |
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A Conjecture on Binary Sequences with the "Trinomial Property" - Cusick, Gong (1999) Self-citation (Gong Sequences) (Correct)
....H is a subset of I , the set of coset leaders of the cyclotomic cosets modulo p. Here we always suppose that 1 2 H . Let B i;t = Tr m t 1 (fi t ff it ) andB t = fB i;t g i0 : 4) Then A = P t2H B t . A useful discussion of these facts is given in [3] The following results were proved in [2]. Theorem 1 A pair ( 0 ) is a trinomial pair of the sequence fa i g if and only if ff is a root of F t (x) 1 x) t 1 x t (5) for each t 2 H and ( 0 ) satisfies 1 ff = ff 0 . Corollary 1 If ( 0 ) is a trinomial pair of the sequence fa i g, then ( 2 j ; ....
....2 are called the regular trinomial pairs of fa i g; other trinomial pairs are called non regular trinomial pairs of fa i g. 3 A Conjecture For all n 3, there exist regular trinomial pairs. A complete search for 3 n 17 was carried out by Golomb and Gong; there are tables for 3 n 12 in [2]. Recall that I is the set of coset leaders modulo 2 n Gamma 1. For t and 2 I , we define two maps on GF(2 n ) as follows, Add 1 map : A(ff) 1 ff; Power map : P t (ff) ff t : Notice that P t AP (ff) 1 ff ) t ; 6) AP t P (ff) 1 ff t ; 7) and P t P = ....
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S. W. Golomb and G. Gong, Periodic binary sequences with the "Trinomial Property",IEEE Trans. on Inform. Theory, vol. 45, No. 4, May 1999, pp. 1276-1279.
Periodic Binary Sequences with the "Trinomial Property" - Golomb, Gong (1998) (1 citation) Self-citation (Golomb Gong With) (Correct)
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S.W. Golomb and G. Gong, Periodic sequences with the "Trinomial Property", 1997 IEEE International Symposium on Information Theory, June 29 - July 4, 1997, Ulm, Germany.
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