Strongly regular graphs from reducible cyclic codes

被引：5

作者：

Shi, Minjia ^{[1
]}

Helleseth, Tor ^{[2
]}

Sole, Patrick ^{[3
]}

机构：

[1] Anhui Univ, Sch Math Sci, Key Lab Intelligent Comp & Signal Proc, Minist Educ, Hefei 230601, Peoples R China

[2] Univ Bergen, Dept Informat, Selmer Ctr, Bergen, Norway

[3] Univ Aix Marseille, CNRS, Cent Marseille, I2M, Marseille, France

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2022年 / 55卷 / 01期

基金：

中国国家自然科学基金;

关键词：

2-weight codes; Reducible cyclic codes; Strongly regular graphs;

D O I：

10.1007/s10801-020-01006-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be a prime number. Reducible cyclic codes of rank 2 over Z(pm) are shown to have exactly two Hamming weights in some cases. Their weight distribution is computed explicitly. When these codes are projective, the coset graphs of their dual codes are strongly regular. The spectra of these graphs are determined.

引用

页码：173 / 184

页数：12

共 17 条

[1]

[Anonymous], TABLE STRONGLY REGUL

[2] WEIGHTS OF IRREDUCIBLE CYCLIC CODES [J].

BAUMERT, LD ;

MCELIECE, RJ .

INFORMATION AND CONTROL, 1972, 20 (02) :158-&

[3] SOME NEW 2-WEIGHT CODES AND STRONGLY REGULAR GRAPHS [J].

BROUWER, AE .

DISCRETE APPLIED MATHEMATICS, 1985, 10 (01) :111-114

[4]

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

[5] Ring geometries, two-weight codes, and strongly regular graphs [J].

Byrne, Eimear ;

Greferath, Marcus ;

Honold, Thomas .

DESIGNS CODES AND CRYPTOGRAPHY, 2008, 48 (01) :1-16

[6] Properties of codes with two homogeneous weights [J].

Byrne, Eimear ;

Kiermaier, Michael ;

Sneyd, Alison .

FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (04) :711-727

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

CALDERBANK, R ;

KANTOR, WM .

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

[8]

Delsarte Ph., 1972, Discrete Mathematics, V3, P47, DOI 10.1016/0012-365X(72)90024-6

[9]

Huffman W. C., 2003, Fundamentals of Error-Correcting Codes

[10]

Neumaier A., 1989, ERGEBNISSE MATH IHRE, V18

← 1 2 →