Some new periodic Golay pairs
نویسندگان
چکیده
منابع مشابه
Golay complementary array pairs
Constructions and nonexistence conditions for multi-dimensional Golay complementary array pairs are reviewed. A construction for a d-dimensional Golay array pair from a (d+1)-dimensional Golay array pair is given. This is used to explain and expand previously known constructive and nonexistence results in the binary case.
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A k-ary charm bracelet is an equivalence class of length n strings with the action on the indices by the additive group of the ring of integers modulo n extended by the group of units. By applying an O(n3) amortized time algorithm to generate charm bracelet representatives with a specified content, we construct 29 new periodic Golay pairs of length 68.
متن کاملQuaternary Golay sequence pairs I: even length
The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the three-stage construction of Fiedler, Jedwab and Parker [FJP08] involving multi-dimensional Golay arrays, and a “sum-difference” construction that modifies a result due to Eliahou, Kervaire and Saffari [EKS91]. The existence of 4-phase seed pairs of lengths ...
متن کاملQuaternary Golay sequence pairs II: odd length
A 4-phase Golay sequence pair of length s ≡ 5 (mod 8) is constructed from a Barker sequence of the same length whose even-indexed elements are prescribed. This explains the origin of the 4-phase Golay seed pairs of length 5 and 13. The construction cannot produce new 4-phase Golay sequence pairs, because there are no Barker sequences of odd length greater than 13. A partial converse to the cons...
متن کاملNegaperiodic Golay pairs and Hadamard matrices
Apart from the ordinary and the periodic Golay pairs, we define also the negaperiodic Golay pairs. (They occurred first, under a different name, in a paper of Ito.) If a Hadamard matrix is also a Toeplitz matrix, we show that it must be either cyclic or negacyclic. We investigate the construction of Hadamard (and weighing matrices) from two negacyclic blocks (2N-type). The Hadamard matrices of ...
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ژورنال
عنوان ژورنال: Numerical Algorithms
سال: 2014
ISSN: 1017-1398,1572-9265
DOI: 10.1007/s11075-014-9910-4