Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding
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State Key Laboratory of Integrated Service Networks, Xidian University, Xi’ an 710071, China
2
Guangxi Key Lab of Multi-Source Information Mining & Security, Guangxi Normal University, Guilin 541004, China
*
Authors to whom correspondence should be addressed.
Academic Editor: Boris Ryabko
Entropy 2021, 23(3), 323; https://doi.org/10.3390/e23030323
Received: 29 December 2020
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Revised: 21 February 2021
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Accepted: 26 February 2021
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Published: 9 March 2021
(This article belongs to the Section Information Theory, Probability and Statistics)
In this paper, we study the entropy functions on extreme rays of the polymatroidal region which contain a matroid, i.e., matroidal entropy functions. We introduce variable strength orthogonal arrays indexed by a connected matroid M and positive integer v which can be regarded as expanding the classic combinatorial structure orthogonal arrays. It is interesting that they are equivalent to the partition-representations of the matroid M with degree v and the
Keywords:
entropy function; matroidal entropy function; matroid; orthogonal array; variable strength orthogonal array; almost affine code; MDS code; polymatroid
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MDPI and ACS Style
Chen, Q.; Cheng, M.; Bai, B. Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding. Entropy 2021, 23, 323. https://doi.org/10.3390/e23030323
AMA Style
Chen Q, Cheng M, Bai B. Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding. Entropy. 2021; 23(3):323. https://doi.org/10.3390/e23030323
Chicago/Turabian StyleChen, Qi, Minquan Cheng, and Baoming Bai. 2021. "Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding" Entropy 23, no. 3: 323. https://doi.org/10.3390/e23030323
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