# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
On sequences with zero autocorrelation. (English) Zbl 0808.05021

Summary: Normal sequences of lengths $n=18,19$ are constructed. It is proved through an exhaustive search that normal sequences do not exist for $n=17,21,22,23$. Marc Gysin has shown that normal sequences do not exist for $n=24$. So the first unsettled case is $n=27$.

Base sequences of lengths $2n-1,2n-1,n,n$ are constructed for all decompositions of $6n-2$ into four squares for $n=2,4,6,\cdots ,20$ and some base sequences for $n=22,24$ are also given. So T-sequences (T-matrices) of length 71 are constructed here for the first time. This gives new Hadamard matrices of orders 213, 781, 1349, 1491, 1633, 2059, 2627, 2769, 3479, 3763, 4331, 4899, 5467, 5609, 5893, 6177, 6461, 6603, 6887, 7739, 8023, 8591, 9159, 9443, 9727, 9869.

##### MSC:
 05B20 Matrices (incidence, Hadamard, etc.) 68R05 Combinatorics in connection with computer science 62H20 Statistical measures of associations