

A158763


Number of equivalence classes of nearnormal 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.914, where "n" in the table is 2n as indexed in this sequence. We introduce a canonical form for nearnormal 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 Tsequences from base sequences. Nearnormal 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)^(i1) for 1 <= i <= n and b_n+1 = a_n+1. Moreover it is required that the sum of the nonperiodic 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), 331. 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), 515.
C. H. Yang, On composition of foursymbol deltacodes and Hadamard matrices, Proc. Amer. Math. Soc. 107 (1989), 763776.


LINKS

Table of n, a(n) for n=1..20.
Dragomir Z. Djokovic, Classification of nearnormal 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



