Gauss periods and codebooks from generalized cyclotomic sets of order four

被引：19

作者：

Hu, Liqin ^{[1
]}

Yue, Qin ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2013年 / 69卷 / 02期

关键词：

Gauss period; Codebook; Generalized cyclotomy; COMPLEX CODEBOOKS; DIFFERENCE SETS;

D O I：

10.1007/s10623-012-9648-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Let p, q be distinct primes with gcd(p - 1, q - 1) = 4. Let D (0), D (1), D (2), D (3) be Whiteman's generalized cyclotomic classes, satisfying the multiplicative group . In this paper, we give formulas of Gauss periods: and , where is a pqth primitive root of unity. As an application, we get the maximum cross-correlation amplitudes of three codebooks from generalized cyclotomic sets of order four and supply conditions on p and q such that they nearly meet the Welch bound.

引用

页码：233 / 246

页数：14

共 21 条

[1] Gauss periods and codebooks from generalized cyclotomic sets of order four
Liqin Hu
Qin Yue
Designs, Codes and Cryptography, 2013, 69 : 233 - 246
[2] GAUSS PERIODS AND CYCLIC CODES FROM CYCLOTOMIC SEQUENCES OF SMALL ORDERS
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Yue Qin
Zhu Xiaomeng
Journal of Electronics(China), 2014, 31 (06) : 537 - 546
[3] The linear complexity of new generalized cyclotomic binary sequences of order four
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[8] On the Linear Complexity of Ding-Helleseth Generalized Cyclotomic Binary Sequences of Order Four and Six
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Cryptography and Communications, 2016, 8 : 605 - 616
[10] Generalized cyclotomic numbers of order two and their applications
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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2016, 8 (04): : 605 - 616

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