Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 2 (2018), 243-251.

The truncated and supplemented Pascal matrix and applications

Michael Hua, Steven B. Damelin, Jeffrey Sun, and Mingchao Yu

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Abstract

In this paper, we introduce the k×n (with kn) truncated, supplemented Pascal matrix, which has the property that any k 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.

Article information

Source
Involve, Volume 11, Number 2 (2018), 243-251.

Dates
Received: 17 February 2016
Revised: 21 July 2016
Accepted: 15 December 2016
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513775060

Digital Object Identifier
doi:10.2140/involve.2018.11.243

Mathematical Reviews number (MathSciNet)
MR3733955

Zentralblatt MATH identifier
06817018

Subjects
Primary: 05B30: Other designs, configurations [See also 51E30] 05B35: Matroids, geometric lattices [See also 52B40, 90C27] 94B25: Combinatorial codes
Secondary: 05B05: Block designs [See also 51E05, 62K10] 05B15: Orthogonal arrays, Latin squares, Room squares 11K36: Well-distributed sequences and other variations 11T71: Algebraic coding theory; cryptography

Keywords
matroid Pascal network coding code MDS maximum distance separable

Citation

Hua, Michael; Damelin, Steven B.; Sun, Jeffrey; Yu, Mingchao. The truncated and supplemented Pascal matrix and applications. Involve 11 (2018), no. 2, 243--251. doi:10.2140/involve.2018.11.243. https://projecteuclid.org/euclid.involve/1513775060


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