On a conjecture of Helleseth regarding pairs of binary m-sequences

被引：17
作者：
Calderbank, AR
McGuire, G
Poonen, B
Rubinstein, M
机构：
[1] CALTECH,DEPT MATH,PASADENA,CA 91125
[2] MATH SCI RES INST,BERKELEY,CA 94720
[3] PRINCETON UNIV,DEPT MATH,PRINCETON,NJ 08544
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 1996年 / 42卷 / 03期
基金：
美国国家科学基金会;
关键词：
binary m-sequences; cyclic codes; crosscorrelation functions;
D O I：
10.1109/18.490561
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Binary m-sequences are maximal-length sequences generated by shift registers of length m, that are employed in navigation, radar, and spread-spectrum communication, It is well known that given a pair of distinct m-sequences, the crosscorrelation function must take on at least three values, This correspondence addresses a conjecture made by Helleseth in 1976, that if m is a power of 2, then there are no pairs of binary m-sequences with a 3-valued crosscorrelation function. This conjecture is proved under the assumption that the three correlation values are symmetric about -1.
引用
收藏
页码：988 / 990
页数：3
相关论文
共 13 条
[1]  
CALDERBANK AR, 1984, PHILIPS J RES, V39, P143
[2]   THE GEOMETRY OF M-SEQUENCES - 3-VALUED CROSS-CORRELATIONS AND QUADRICS IN FINITE PROJECTIVE GEOMETRY [J].
GAMES, RA .
SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1986, 7 (01) :43-52
[3]   THE GEOMETRY OF QUADRICS AND CORRELATIONS OF SEQUENCES [J].
GAMES, RA .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1986, 32 (03) :423-426
[4]   MAXIMAL RECURSIVE SEQUENCES WITH 3-VALUED RECURSIVE CROSS-CORRELATION FUNCTIONS [J].
GOLD, R .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1968, 14 (01) :154-+
[5]  
Golomb S. W., 1982, Shift Register Sequences
[6]   THEORY OF TRANSFORMATION GROUPS OF POLYNOMIALS OVER GF(2) WITH APPLICATIONS TO LINEAR SHIFT REGISTER SEQUENCES [J].
GOLOMB, SW .
INFORMATION SCIENCES, 1968, 1 (01) :87-&
[7]   SOME RESULTS ABOUT CROSS-CORRELATION FUNCTION BETWEEN 2 MAXIMAL LINEAR SEQUENCES [J].
HELLESETH, T .
DISCRETE MATHEMATICS, 1976, 16 (03) :209-232
[8]  
KASAMI T, 1969, P C COMB MATH ITS AP, P335
[9]  
MacWilliams F. J., 1977, THEORY ERROR CORRECT
[10]  
MCELIECE RJ, 1971, J COMB THEORY, V10, P80, DOI [10.1016/0097-3165(71)90066-5, DOI 10.1016/0097-3165(71)90066-5]
12