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The truncated
and supplemented Pascal matrix and applications
Michael Hua, Steven B. Damelin, Jeffrey Sun and Mingchao Yu
Vol. 11 (2018), No. 2, 243–251
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Abstract |
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In this paper, we introduce the (with ) truncated, supplemented Pascal matrix, which has the property that any columns form a linearly independent set. This property is also present in Reed–Solomon codes; however, Reed–Solomon codes are completely dense, whereas the truncated, supplemented Pascal matrix has multiple zeros. If the maximum distance separable code conjecture is correct, then our matrix has the maximal number of columns (with the aforementioned property) that the conjecture allows. This matrix has applications in coding, network coding, and matroid theory. |
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Keywords
matroid, Pascal, network, coding, code, MDS, maximum
distance separable
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Mathematical Subject Classification 2010
Primary: 05B30, 05B35, 94B25
Secondary: 05B05, 05B15, 11K36, 11T71
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Milestones
Received: 17 February 2016
Revised: 21 July 2016
Accepted: 15 December 2016
Published: 17 September 2017
Communicated by Jim Haglund
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Authors |
| Michael Hua | |
| Department of Nuclear Engineering
and Radiological Sciences and Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| Steven B. Damelin | |
| Mathematical Reviews The American Mathematical Society Ann Arbor, MI United States |
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| Jeffrey Sun | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| Mingchao Yu | |
| College of Engineering and Computer
Science Australian National University Canberra Australia |
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