# On sequences with zero autocorrelation

@article{Koukouvinos1994OnSW, title={On sequences with zero autocorrelation}, author={Christos Koukouvinos and Stratis Kounias and Jennifer Seberry and C. H. Yang and Y. Yang}, journal={Designs, Codes and Cryptography}, year={1994}, volume={4}, pages={327-340} }

Normal sequences of lengthsn=18, 19 are constructed. It is proved through an exhaustive search that normal sequences do not exist forn=17, 21, 22, 23. Marc Gysin has shown that normal sequences do not exist forn=24. So the first unsettled case isn=27.Base sequences of lengths 2n−1, 2n−1,n,n are constructed for all decompositions of 6n−2 into four squares forn=2, 4, 6, ..., 20 and some base sequences forn=22, 24 are also given. So T-sequences (T-matrices) of length 71 are constructed here for… Expand

#### 25 Citations

On Sequences with Zero Autocorrelation and Orthogonal Designs

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2001

The proposed methods for multiplying the length and type of sequences with elements on a set of commuting variables which have zero non-periodic autocorrelation function lead to the construction of many new orthogonal designs. Expand

Multiplication of sequences with zero autocorrelation

- Mathematics, Computer Science
- Australas. J Comb.
- 1994

Near normal sequences of new lengths n = 4m + 1 = 49,53,57 are constructed and a reformulation of Yang's powerful theorems on T-sequences is given. Expand

A construction of binary Golay sequence pairs from odd‐length Barker sequences

- Mathematics
- 2009

Binary Golay sequence pairs exist for lengths 2, 10 and 26 and, by Turyn’s product construction, for all lengths of the form 2 a 10 b 26 c where a,b,c are non-negative integers. Computer search has… Expand

On weighing matrices

- Mathematics
- 1993

We give new sets of {0, 1, -1} sequences with zero autocorrelation function, new constructions for weighing matrices and review the weighing matrix conjecture for orders 4t, t є {1,...,25}… Expand

New classes of orthogonal designs and weighing matrices derived from near normal sequences

- Mathematics, Computer Science
- Australas. J Comb.
- 2010

It is shown that near normal sequences of length n = 4m + 1 can be used to construct four directed sequences of lengths 2m+1, 2m-1,2m, 2 m and type (n, n) with zero NPAF, which leads to the construction of many large orthogonal designs. Expand

Classification of normal sequences

- Mathematics
- 2010

Base sequences BS(m,n) are quadruples (A;B;C;D) of {+1,-1}-sequences, with A and B of length m and C and D of length n, such that the sum of their nonperiodic autocorrelation functions is a… Expand

New results with near- Yang sequences

- Mathematics
- 1994

We construct new TW -sequences, weighing matrices and orthogonal designs using near-Yang sequences. In particular we construct new OD(60(2m + 1) + 4t; 13(2m+ 1), 13(2m+ 1), 13(2m+ 1), 13(2m+ 1) and… Expand

On ternary complementary pairs

- Mathematics, Computer Science
- Australas. J Comb.
- 2001

A variety of new constructions which concatenate shorter groups of sequences to obtain longer sequences to give many new restrictions on TCP's of lengths £ and deficiencies 8 = 2x, where x == £ mod 4. Expand

Amicable matrices and orthogonal designs

- Mathematics
- 2015

This thesis is mainly concerned with the orthogonal designs of Baumert-Hall array type, OD(4n;n,n,n,n) where n = 2k, k is odd integer. For every odd prime power pr, we construct an infinite class of… Expand

New normal sequences of length 25

- Mathematics
- 1995

An introduction to binary sequences, combi natorial designs and how they are related to communication theory and computer security is given. An exhaustive search algorithm for normal sequences is… Expand

#### References

SHOWING 1-10 OF 23 REFERENCES

A survey of base sequences, disjoint complementary sequences and OD(4t; t, t, t, t)

- Mathematics
- 1989

We survey the existence of base sequences, that is four sequences of lengths m + p, m + p, m, m, p odd with zero auto correlation function which can be used with Yang numbers and four disjoint… Expand

Addendum to further results on base sequences, disjoint complementary sequences, OD(4t; t, t, t, t) and the excess of Hadamard matrices

- 1991

It is known that if there are base sequences of lengths m + p, m + p, m, m and y is a Yang number then there are T-sequences of length (2m + p)y. Let G = {g : g = 2a10b26c, a, b, c non negative… Expand

Hadamard matrices, finite sequences, and polynomials defined on the unit circle

- Mathematics
- 1979

If a (*)-type Hadamard matrix of order 2n (i.e. a pair (A, B) of n X n circulant (1, 1) matrices satisfying AA' + BB' = 2nI) exists and a pair of Golay complementary sequences (or equivalently,… Expand

Hadamard Matrices and δ-Codes of Length 3n

- Physics
- 1982

It is found that four-symbol 6-codes of length t = 3n can be composed for odd n 0. Consequently new families of Hadamard matrices of orders 4tw and 20tw can be constructed, where w is the order of… Expand

Lagrange identity for polynomials and -codes of lengths 7 and 13

- Mathematics
- 1983

It is known that application of the Lagrange identity for polynomials (see [I]) is the key to composing four-symbol 8-codes of length (2s + I)t for s -2a 10"26' and odd t s 59 or t = 2dlI0e26f + 1,… Expand

On Golay sequences

- Computer Science, Mathematics
- Discret. Math.
- 1991

It is proved that Golay sequences of length n = 2 · 7 2 t do not exist and new proofs of some known results are given and conjecture that there are no Golays of length 2 · q 2 t where q is not the sum of two integer squares. Expand

On Composition of Four-Symbol δ-Codes and Hadamard Matrices

- Mathematics
- 1989

It is shown that key instruments for composition of four-symbol 6-codes are the Lagrange identity for polynomials, a certain type of quasisymmetric sequences (i.e., a set of normal or near normal… Expand

Hadamard matrices, Sequences, and Block Designs

- Mathematics
- 1992

One hundred years ago, in 1893, Jacques Hadamard [31] found square matrices of orders 12 and 20, with entries ±1, which had all their rows (and columns) pairwise orthogonal. These matrices, X =… Expand

A construction for Hadamard arrays

- Mathematics
- 1972

We give a construction for Hadamard arrays and exhibit the arrays of orders 4t , tE{l,3,5,7, ... 19} This gives seventeen new Hadamard matrices of order less than 4000. Disciplines Physical Sciences… Expand

ON BASE AND TURYN SEQUENCES

- Mathematics
- 1990

Base sequences of lengths n + 1, n + 1, n , n are constructed for all decompositions of 4/1 + 2 into four squares for n = 19,... , 24. The construction is achieved through an algorithm which is also… Expand