Symbol-pair weight distribution of some irreducible cyclic codes

被引：0

作者：

Maouche, Youcef ^{[1
]}

机构：

[1] Univ Sci & Technol Houari Boumediene, Dept Math, Algiers, Algeria

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2023年 / 15卷 / 01期

关键词：

Irreducible cyclic codes; Symbol-pair weight; Trace codes; Gauss sums; Cyclotomic numbers; HAMMING WEIGHTS;

D O I：

10.1007/s12095-022-00599-y

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we study the symbol-pair weight distribution of some irreducible cyclic codes. We define generalized cyclotomic numbers and provide some of their properties. Using a character sum, we establish a relationship among the symbol-pair weight of irreducible cyclic codes, generalized cyclotomic numbers and the Gaussian periods. Moreover, we determine the symbol-pair weight distribution of some classes of irreducible cyclic codes.

引用

页码：209 / 220

页数：12

共 12 条

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

BAUMERT, LD ;

MCELIECE, RJ .

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

[2]

Berndt B., 1998, Gauss and Jacobi Sums

[3]

Cassuto Y, 2011, IEEE INT SYMP INFO

[4] Codes for Symbol-Pair Read Channels [J].

Cassuto, Yuval ;

Blaum, Mario .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (12) :8011-8020

[5] Codes for Symbol-Pair Read Channels [J].

Cassuto, Yuval ;

Blaum, Mario .

2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2010, :988-992

[6] Hamming weights in irreducible cyclic codes [J].

Ding, Cunsheng ;

Yang, Jing .

DISCRETE MATHEMATICS, 2013, 313 (04) :434-446

[7] The Weight Distribution of Some Irreducible Cyclic Codes [J].

Ding, Cunsheng .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (03) :955-960

[8]

MACWILLIAMS J, 1981, IEEE T INFORM THEORY, V27, P796, DOI 10.1109/TIT.1981.1056420

[9] PERIOD POLYNOMIALS AND GAUSS SUMS FOR FINITE-FIELDS [J].

MYERSON, G .

ACTA ARITHMETICA, 1981, 39 (03) :251-264

[10] Geometric Approach to b-Symbol Hamming Weights of Cyclic Codes [J].

Shi, Minjia ;

Ozbudak, Ferruh ;

Sole, Patrick .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2021, 67 (06) :3735-3751

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