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Constructions of External Difference Families and Disjoint Difference Families

# Constructions of External Difference Families and Disjoint Difference Families,10.1007/s10623-006-0005-7,Designs, Codes and Cryptography,Yanxun Chang,

Constructions of External Difference Families and Disjoint Difference Families
.  External difference families (EDFs) are a type of new combinatorial designs originated from cryptography. In this paper, some earlier ideas of recursive and cyclotomic constructions of combinatorial designs are extended, and a number of classes of EDFs and disjoint difference families are presented. A link between a subclass of EDFs and a special type of (almost) difference sets is set up.
Journal: Designs, Codes and Cryptography - DCC , vol. 40, no. 2, pp. 167-185, 2006
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## Citation Context (4)

• ...Difference families are well studied and have applications in coding theory and cryptography (Chang and Ding 2006); Chen et al...

### Cunsheng Ding, et al. Zero-Difference Balanced Functions With Applications

• ...The following lemma is useful in the next theorem. Lemma 3.5 ([2]) Let p be an odd prime...
• ...� α 2 ,α 5 ,...,α 3t−1 � . Then from [2], � Q0 +� Q1 +� Q2 = (t − 1)Z ∗ ...

### Jianguo Lei, et al. Optimal difference systems of sets and partition-type cyclic differenc...

• ...Proof. For such n, there exist both an (n;3;2)-DDF over Zn and a (4n;3;2)-DDF over Z4n (see [1])...
• ...Proof. (a) Since for any odd integer n, there exists a perfect regular DSS(n;2; n¡1 2 ; n ¡ 3) (see [1])...

### Cuiling Fan, et al. Constructions of optimal difference systems of sets

• ...<{[SECTION]}>[5] A. B. Carleial, “A case where interference does not reduce capacity,”...
• ...Chang and Ding [5] established a link between a subset of EDFs and a subset of DDFs...
• ...Lemma 5.1 [5]: Let be an abelian group of order , and let be a collection of -subsets of .I f is a partition of , then is a -EDF over if and only if it is a -DDF over . For any odd , there exists a -DDF [5]...
• ...Lemma 5.1 [5]: Let be an abelian group of order , and let be a collection of -subsets of .I f is a partition of , then is a -EDF over if and only if it is a -DDF over . For any odd , there exists a -DDF [5]...
• ...Lemma 5.6 [5]: Let and be two positive integers...

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## Citations (9)

### Zero-Difference Balanced Functions With Applications

Published in 2012.

### Optimal difference systems of sets and partition-type cyclic difference packings(Citations: 1)

Journal: Designs, Codes and Cryptography - DCC , vol. 58, no. 2, pp. 135-153, 2011

### Constructions of optimal difference systems of sets

Journal: Science China-mathematics - SCI CHINA-MATH , vol. 54, no. 1, pp. 173-184, 2011

### Perfect difference systems of sets and Jacobi sums(Citations: 2)

Journal: Discrete Mathematics - DM , vol. 309, no. 12, pp. 3954-3961, 2009

### Cyclotomic constructions of external difference families and disjoint difference families

Journal: Journal of Combinatorial Designs - J COMB DES , vol. 17, no. 4, pp. 333-341, 2009