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A158763 Number of equivalence classes of near-normal sequences NN(2n). 0
1, 2, 2, 3, 8, 14, 11, 24, 20, 18, 32, 12, 3, 20, 9, 8, 5, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of rows of Table 1 of Djokovic, pp.9-14, where "n" in the table is 2n as indexed in this sequence. We introduce a canonical form for near-normal sequences NN(n), and using it we enumerate the equivalence classes of such sequences for even n up to 30. These sequences are needed for Yang multiplication in the construction of longer T-sequences from base sequences. Near-normal sequences were introduced by C.H. Yang. They can be viewed as quadruples of binary sequences (A;B;C;D) where A and B have length n + 1, while C and D have length n, and n has to be even. By definition, the sequences A = a_1, a_2, . . ., a_n+1 and B = b_1, b_2, . . ., b_n+1 are related by the equalities b_i = (-1)^(i-1) for 1 <= i <= n and b_n+1 = -a_n+1. Moreover it is required that the sum of the non-periodic autocorrelation functions of the four sequences be a delta function. Examples of near-

REFERENCES

D. Z. Djokovic, Aperiodic complementary quadruples of binary sequences, JCMCC 27 (1998), 3-31. Correction: ibid 30 (1999), p. 254. C. Koukouvinos, S. Kounias, J. Seberry, C.H. Yang and J. Yang, Multiplication of sequences with zero autocorrelation, Austral. J. Combin. 10 (1994), 5-15.

C. H. Yang, On composition of four-symbol delta-codes and Hadamard matrices, Proc. Amer. Math. Soc. 107 (1989), 763-776.

LINKS

Table of n, a(n) for n=1..20.

Dragomir Z. Djokovic, Classification of near-normal sequences, Mar 25, 2009.

Dragomir Z. Djokovic, Hadamard matrices of small order and Yang conjecture, Mar 25, 2009.

D. Z. Djokovic, A new Yang number and consequences, Designs, Codes and Cryptography 54:3 (2010). arXiv:1007.5434

CROSSREFS

Sequence in context: A227380 A159789 A153932 * A001131 A019177 A153941

Adjacent sequences:  A158760 A158761 A158762 * A158764 A158765 A158766

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Mar 26 2009

EXTENSIONS

5 more terms from the second Djokovic link, sent by Jonathan Vos Post and William P. Orrick, Jan 02 2010

STATUS

approved

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Last modified November 20 12:30 EST 2017. Contains 294971 sequences.