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

Mathematical Sciences

Georgia Southern University
The Pennsylvania State University

Research output: Contribution to journal › Article › peer-review

10 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
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

Scopus Subject Areas

General Mathematics

Keywords

(t, m, s)-net
Binary vector
Hypercube
Linear code
Linear independence
Orthogonal array
Orthogonal structure
Pseudo (t, m, s)-net

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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 - Michalski, G.

AU - Mullen, G. L.

AU - Stone, D.

PY - 2004/4

Y1 - 2004/4

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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.

KW - (t, m, s)-net

KW - Binary vector

KW - Hypercube

KW - Linear code

KW - Linear independence

KW - Orthogonal array

KW - Orthogonal structure

KW - Pseudo (t, m, s)-net

UR - https://www.scopus.com/pages/publications/2142786713

U2 - 10.1007/s00605-003-0044-3

DO - 10.1007/s00605-003-0044-3

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ER -

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

Scopus Subject Areas

Keywords

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