Abstract
A t-spontaneous emission error design, called t-SEED for short, is a combinatorial design introduced by Beth et al. (Des Codes Cryptogr 29:51–70, 2003) in relation to a quantum jump code. In this article, firstly, it is shown that an optimal t-SEED attaining a given upper bound is a large set of Steiner t-designs. Secondly, we present some recursive constructions of t-SEEDs. Moreover, an application to secret sharing scheme by utilizing the properties of a t-SEED is also discussed.
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Acknowledgments
We would like to thank the anonymous reviewers for the valuable comments, which was very helpful to improve the paper considerably. The work of M. Jimbo was supported in part by JSPS under Grant-in-Aid for Scientific Research (B)22340016 and Grant-in-Aid for Challenging Exploratory Research 22654031.
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Communicated by D. Jungnickel.
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Lin, Y., Jimbo, M. Extremal properties of t-SEEDs and recursive constructions. Des. Codes Cryptogr. 73, 805–823 (2014). https://doi.org/10.1007/s10623-013-9829-0
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DOI: https://doi.org/10.1007/s10623-013-9829-0