Hadamard partitioned difference families and their descendants

被引：12
|
作者：
Buratti, Marco [1 ]
机构：
[1] Univ Perugia, Dipartimento Matemat & Informat, Via Vanvitelli 1, I-06123 Perugia, Italy
来源：
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2019年 / 11卷 / 04期
关键词：
Partitioned difference family; Hadamard difference set; Strong difference family;
D O I：
10.1007/s12095-018-0308-3
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
If D is a (4u2,2u2-u,u2-u) Hadamard difference set (HDS) in G, then {G,G\D} is clearly a (4u2,[2u2-u,2u2+u],2u2) partitioned difference family (PDF). Any (v,K,)-PDF will be said a Hadamard PDF if v=2 as the one above. We present a doubling construction which, starting from any Hadamard PDF, leads to an infinite class of PDFs. As a special consequence, we get a PDF in a group of order 4u2(2n+1) and three block-sizes 4u2-2u, 4u2 and 4u2+2u, whenever we have a (4u2,2u2-u,u2-u)-HDS and the maximal prime power divisors of 2n+1 are all greater than 4u2+2u.
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页码：557 / 562
页数：6
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