Cyclotomic construction of strong external difference families in finite fields

被引：13
|
作者：
Wen, Jiejing [1 ]
Yang, Minghui [2 ]
Fu, Fangwei [1 ]
Feng, Keqin [3 ]
机构：
[1] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China
[2] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100193, Peoples R China
[3] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2018年 / 86卷 / 05期
关键词：
Strong external difference family; Difference set; Partial difference set; Cyclotomic class; Cyclotomic number; Finite field; Strong algebraic manipulation detection code; SETS;
D O I：
10.1007/s10623-017-0384-y
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Strong external difference families (SEDFs) and their generalizations GSEDFs and BGSEDFs in a finite abelian group G are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891-2906, 2016) and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using difference sets and partial difference sets in G. Then, as applications of the general constructions, we construct series of SEDF, GSEDF and BGSEDF in finite fields by using cyclotomic classes. Particularly, we present an -SEDF in by using the cyclotomic classes of order 11 in which answers an open problem raised in Paterson and Stinson (2016).
引用
收藏
页码：1149 / 1159
页数：11
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