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Generic constructions for partitioned difference families with applications: a unified combinatorial approach

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Abstract

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.

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Acknowledgments

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, Zhejiang, China

    Shuxing Li

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Hengjia Wei & Gennian Ge

  3. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048, China

    Gennian Ge

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  1. Shuxing Li
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  2. Hengjia Wei
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  3. Gennian Ge
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Correspondence to Gennian Ge.

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Communicated by K. T. Arasu.

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Li, S., Wei, H. & Ge, G. Generic constructions for partitioned difference families with applications: a unified combinatorial approach. Des. Codes Cryptogr. 82, 583–599 (2017). https://doi.org/10.1007/s10623-016-0182-y

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  • DOI: https://doi.org/10.1007/s10623-016-0182-y

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