Partitioned difference families: The storm has not yet passed

Marco Buratti; Dieter Jungnickel

doi:10.3934/amc.2021030

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2023, Volume 17, Issue 4: 928-934. Doi: 10.3934/amc.2021030

This issue Previous Article On the number of factorizations of $ t $ mod $ N $ and the probability distribution of Diffie-Hellman secret keys for many users Next Article A decoding algorithm for 2D convolutional codes over the erasure channel

Partitioned difference families: The storm has not yet passed

Marco Buratti^1, , and
Dieter Jungnickel^2,

1.
Dipartimento di Matematica e Informatica, Università di Perugia, via Vanvitelli 1, 06123 Italy
2.
Mathematical Institute, University of Augsburg, 86135 Augsburg, Germany

^* Corresponding author: Marco Buratti
^* Corresponding author: Marco Buratti

Received: February 2021

Early access: August 2021

Published: August 2023

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Abstract

Two years ago, we alarmed the scientific community about the large number of bad papers in the literature on zero difference balanced functions, where direct proofs of seemingly new results are presented in an unnecessarily lengthy and convoluted way. Indeed, these results had been proved long before and very easily in terms of difference families.

In spite of our report, papers of the same kind continue to proliferate. Regrettably, a further attempt to put the topic in order seems unavoidable. While some authors now follow our recommendation of using the terminology of partitioned difference families, their methods are still the same and their results are often trivial or even wrong. In this note, we show how a very recent paper of this type can be easily dealt with.

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Mathematics Subject Classification: Primary: 05B10.

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References

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