长度为奇素数的完备高斯整数序列构造法

doi:10.11959/j.issn.1000-436x.2018230

Abstract

Abstract:

Constructions of perfect Gaussian integer sequences (PGIS) based on the cyclotomic classes were proposed.The PGIS with degree 3 and 5 were constructed respectively from the cyclotomic classes of order 2 and 4.The presented sequences with odd prime length have ideal autocorrelations.The methods solved the problem that the traditional constructions of PGIS from the cyclotomic classes have high computational complexity.As a result,this kind of sequences will be useful in the applications of wireless communications.

Key words: perfect Gaussian integer sequence, pseudo-random sequence, cyclotomic classes, discrete Fourier transform

CLC Number:

TN911.2

Yubo LI,Miao CHEN,Tao LIU,Ying ZHANG. Constructions of perfect Gaussian integer sequences of odd prime length[J]. Journal on Communications, 2018, 39(11): 190-197.

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References 19

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自由度为3的完备高斯整数序列			自由度为5阶完备高斯整数序列
f	p= 2f +1	(a,b)	f	p= 4f +1	(a,b)
2	5	(±1,±2)(±2,±1)	1	5	(±1,±2)(±2,±1)
3	7	不存在	3	13	(±3,±2)(±2,±3)
5	11	不存在	4	17	(±1,±4)(±4,±1)
6	13	(±3,±2)(±2,±3)	7	29	(±2,±5)(±5,±2)
8	17	(±1,±4)(±4,±1)	9	37	(±1,±6)(±6,±1)
9	19	不存在	10	41	(±4,±5)(±5,±4)
11	23	不存在	13	53	(±2,±7)(±7,±2)
14	29	(±2,±5)(±5,±2)	15	61	(±6,±5)(±5,±6)
15	31	不存在	18	73	(±8,±3)(±3,±8)
18	37	(±1,±6)(±6,±1)	22	89	(±8,±5)(±5,±8)
20	41	(±4,±5)(±5,±4)	24	97	(±4,±9)(±9,±4)
21	43	不存在	25	101	(±1,±10)(±10,±1)
23	47	不存在	27	109	(±3,±10)(±10,±3)

Constructions of perfect Gaussian integer sequences of odd prime length

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(j,k)₄	0	1	2	3
0	A	B	C	D
1	E	E	D	B
2	A	E	A	E
3	E	D	B	E

(j,k)₄	0	1	2	3
0	A	B	C	D
1	B	D	E	E
2	C	E	C	E
3	D	E	E	B