The Number of Linearly Independent Binary Vectors with Applications to the Construction of Hypercubes and Orthogonal Arrays, Pseudo (t, m, s)-Nets and Linear Codes

S. B. Damelin; G. Michalski; G. L. Mullen; D. Stone

doi:10.1007/s00605-003-0044-3

The Number of Linearly Independent Binary Vectors with Applications to the Construction of Hypercubes and Orthogonal Arrays, Pseudo (t, m, s)-Nets and Linear Codes

S. B. Damelin, G. Michalski, G. L. Mullen, D. Stone

Mathematics

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9 Scopus citations

Abstract

We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1 ≤ k ≤ n. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.

Original language	English (US)
Pages (from-to)	277-288
Number of pages	12
Journal	Monatshefte fur Mathematik
Volume	141
Issue number	4
DOIs	https://doi.org/10.1007/s00605-003-0044-3
State	Published - Apr 2004

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00605-003-0044-3

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abstract = "We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1 ≤ k ≤ n. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.",

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AU - Mullen, G. L.

AU - Stone, D.

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AB - We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1 ≤ k ≤ n. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.

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The Number of Linearly Independent Binary Vectors with Applications to the Construction of Hypercubes and Orthogonal Arrays, Pseudo (t, m, s)-Nets and Linear Codes

Abstract

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