TY - JOUR
T1 - Generic constructions for partitioned difference families with applications
T2 - a unified combinatorial approach
AU - Li, Shuxing
AU - Wei, Hengjia
AU - Ge, Gennian
N1 - Funding Information:
The first author would like to express his gratitude to Prof. Maosheng Xiong, Hong Kong University of Science and Technology, for the fruitful discussions on this topic. Research supported by the National Natural Science Foundation of China under Grant Nos. 61171198, 11431003 and 61571310, and the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions.
Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - Partitioned difference families are an interesting class of discrete structures which can be used to derive optimal constant composition codes. There have been intensive researches on the construction of partitioned difference families. In this paper, we consider the combinatorial approach. We introduce a new combinatorial configuration named partitioned relative difference family, which proves to be very powerful in the construction of partitioned difference families. In particular, we present two general recursive constructions, which not only include some existing constructions as special cases, but also generate many new series of partitioned difference families. As an application, we use these partitioned difference families to construct several new classes of optimal constant composition codes.
AB - Partitioned difference families are an interesting class of discrete structures which can be used to derive optimal constant composition codes. There have been intensive researches on the construction of partitioned difference families. In this paper, we consider the combinatorial approach. We introduce a new combinatorial configuration named partitioned relative difference family, which proves to be very powerful in the construction of partitioned difference families. In particular, we present two general recursive constructions, which not only include some existing constructions as special cases, but also generate many new series of partitioned difference families. As an application, we use these partitioned difference families to construct several new classes of optimal constant composition codes.
KW - Constant composition codes
KW - Difference matrices
KW - Partitioned difference families
KW - Partitioned relative difference families
KW - Recursive constructions
UR - http://www.scopus.com/inward/record.url?scp=84955620749&partnerID=8YFLogxK
U2 - 10.1007/s10623-016-0182-y
DO - 10.1007/s10623-016-0182-y
M3 - Article
AN - SCOPUS:84955620749
SN - 0925-1022
VL - 82
SP - 583
EP - 599
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 3
ER -