A Class of Optimal Cyclic Codes With Two Zeros

被引：15

作者：

Liao, Dengchuan ^{[1
]}

Kai, Xiaoshan ^{[1
]}

Zhu, Shixin ^{[1
]}

Li, Ping ^{[1
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China

来源：

IEEE COMMUNICATIONS LETTERS | 2019年 / 23卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Minimum distance; cyclic codes; weight distribution; MINIMUM DISTANCE;

D O I：

10.1109/LCOMM.2019.2921330

中图分类号：

TN [电子技术、通信技术];

学科分类号：

0809 ;

摘要：

Let m > 2 be an integer and p be an odd prime. We explore the minimum distance of p-ary cyclic codes of length n = 2(p(m) - 1)/(p - 1) with two zeros. A sufficient condition for such cyclic codes with minimum distance at least three is obtained. A class of optimal p-ary cyclic codes with minimum distance four are presented. Four explicit constructions for such optimal cyclic codes are provided. The weight distribution of the dual of the cyclic code in the first construction is given.

引用

页码：1293 / 1296

页数：4

共 20 条

[1] Linear codes from perfect nonlinear mappings and their secret sharing schemes [J].

Carlet, C ;

Ding, CS ;

Yuan, J .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (06) :2089-2102

[2]

Cary Huffman., 2003, Fundamentals of Error-Correcting Codes

[3] On the minimum distances of non-binary cyclic codes [J].

Charpin, P ;

Tietäväinen, A ;

Zinoviev, V .

DESIGNS CODES AND CRYPTOGRAPHY, 1999, 17 (1-3) :81-85

[4]

Charpin P., 1997, Problems Inf. Transmiss, V33, P3

[5] Planar Functions and Planes of Lenz-Barlotti Class II [J].

Coulter R.S. ;

Matthews R.W. .

Designs, Codes and Cryptography, 1997, 10 (2) :167-184

[6] SUBFIELD SUBCODES OF MODIFIED REED-SOLOMON CODES [J].

DELSARTE, P .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1975, 21 (05) :575-576

[7] Optimal Ternary Cyclic Codes From Monomials [J].

Ding, Cunsheng ;

Helleseth, Tor .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (09) :5898-5904

[8] A q-polynomial approach to cyclic codes [J].

Ding, Cunsheng ;

Ling, San .

FINITE FIELDS AND THEIR APPLICATIONS, 2013, 20 :1-14

[9] A class of optimal ternary cyclic codes and their duals [J].

Fan, Cuiling ;

Li, Nian ;

Zhou, Zhengchun .

FINITE FIELDS AND THEIR APPLICATIONS, 2016, 37 :193-202

[10] A q-polynomial approach to constacyclic codes [J].

Fang, Weijun ;

Wen, Jiejing ;

Fu, Fang-Wei .

FINITE FIELDS AND THEIR APPLICATIONS, 2017, 47 :161-182

← 1 2 →