Constructions of strongly regular Cayley graphs and skew Hadamard difference sets from cyclotomic classes

被引：17

作者：

Feng, Tao ^{[1
]}

Momihara, Koji ^{[2
]}

Xiang, Qing ^{[3
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Kumamoto Univ, Fac Educ, Kumamoto 8608555, Japan

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

COMBINATORICA | 2015年 / 35卷 / 04期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

ASSOCIATION SCHEMES; 2-WEIGHT CODES; GAUSS SUMS;

D O I：

10.1007/s00493-014-2895-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes of finite fields, and they generalize the constructions given by Feng and Xiang [10,12]. Three infinite families of strongly regular graphs with new parameters are obtained. The main tools that we employed are index 2 Gauss sums, instead of cyclotomic numbers.

引用

页码：413 / 434

页数：22

共 28 条

[1]

Baumert L.D., 1973, DSN Progr. Rep, V16, P128

[2] UNIFORM CYCLOTOMY [J].

BAUMERT, LD ;

MILLS, WH ;

WARD, RL .

JOURNAL OF NUMBER THEORY, 1982, 14 (01) :67-82

[3]

Berndt B., 1997, Gauss and Jacobi Sums

[4]

Beth T., 1999, Encyclopedia of Mathematics and Its Applications, V1

[5] Cyclotomy and strongly regular graphs [J].

Brouwer, AE ;

Wilson, RM ;

Xiang, Q .

JOURNAL OF ALGEBRAIC COMBINATORICS, 1999, 10 (01) :25-28

[6]

Brouwer AE, 2012, UNIVERSITEXT, P1, DOI 10.1007/978-1-4614-1939-6

[7] THE GEOMETRY OF 2-WEIGHT CODES [J].

CALDERBANK, R ;

KANTOR, WM .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 :97-122

[8] SOME NEW CYCLOTOMIC STRONGLY REGULAR GRAPHS [J].

DELANGE, CLM .

JOURNAL OF ALGEBRAIC COMBINATORICS, 1995, 4 (04) :329-330

[9] Pseudocyclic and non-amorphic fusion schemes of the cyclotomic association schemes [J].

Feng, Tao ;

Wu, Fan ;

Xiang, Qing .

DESIGNS CODES AND CRYPTOGRAPHY, 2012, 65 (03) :247-257

[10] Strongly regular graphs from unions of cyclotomic classes [J].

Feng, Tao ;

Xiang, Qing .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2012, 102 (04) :982-995

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