Multiplicative difference sets via additive characters

被引：79

作者：

Dillon, JF ^{[1
]}

机构：

[1] Natl Secur Agcy, Ft George G Meade, MD 20755 USA

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 1999年 / 17卷 / 1-3期

关键词：

cyclic difference set; pseudorandom binary sequence; ideal autocorrelation; 3-valued cross-correlation; m-sequence;

D O I：

10.1023/A:1026435428030

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We use Fourier analysis on the additive group of F-2m to give an alternative proof of the recent theorem of Maschietti and to prove recent conjectures of No, Chung and Yun and No, Golomb, Gong, Lee and Gaal on difference sets in the multiplicative group of F-2m, m odd. Along the way we prove a stronger form of a celebrated theorem of Welch on the 3-valued cross-correlation of maximal length sequences.

引用

页码：225 / 235

页数：11

共 18 条

[1]

[Anonymous], 1995, LNCS

[2]

Assmus Jr. E.F., 1992, CAMBRIDGE TRACTS MAT, V103

[3]

Baumert L.D., 1971, CYCLIC DIFFERENCE SE

[4]

BETH T, IN PRESS DESIGN THEO

[5] A CLASS OF EXCEPTIONAL POLYNOMIALS [J].

COHEN, SD ;

MATTHEWS, RW .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 345 (02) :897-909

[6]

DOBBERTIN H, IN PRESS KASAMI POWE

[7]

EVANS R, GAUSS SUMS JACOBI SU

[8]

Hall M., 1986, COMBINATORIAL THEORY

[9] WEIGHT ENUMERATORS FOR SEVERAL CLASSES OF SUBCODES OF 2ND ORDER BINARY REED-MULLER CODES [J].

KASAMI, T .

INFORMATION AND CONTROL, 1971, 18 (04) :369-&

[10] Difference Sets and Hyperovals [J].

Maschietti A. .

Designs, Codes and Cryptography, 1998, 14 (1) :89-98

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