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Hadamard Matrices on Error Detection and Correction: Useful Links to BIBD

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Matrices, Statistics and Big Data (IWMS 2016)

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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Abstract

In the areas of Computer Science and Telecommunications there is a huge amount of applications in which error control, error detection and error correction are crucial tools to enable reliable delivery of digital data over unreliable communication, thus providing quality of service. Hadamard matrices can almost directly be used as an error-correcting code using an Hadamard code, generalized in Reed-Muller codes. Advances in algebraic design theory by using deep connections with algebra, finite geometry, number theory, combinatorics and optimization provided a substantial progress on exploring Hadamard matrices. Their construction and its use on combinatorics are crucial nowadays in diverse fields such as: quantum information, communications, networking, cryptography, biometry and security. Hadamard matrices give rise to a class of block designs named Hadamard configurations and different applications of it based on new technologies and codes of figures such as QR Codes are present almost everywhere. Some connections to Balanced Incomplete Block Designs are very well known as a tool to solve emerging problems in these areas. We will explore the use of Hadamard matrices on QR Codes error detection and correction. Some examples will be provided.

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Notes

  1. 1.

    Jacques Hadamard (1865–1963).

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Acknowledgements

This research was partially sponsored by national funds through the FCT—Fundação para a Ciência e Tecnologia, Portugal—FCT under the project PEst-OE/MAT/UI0006/2013 (CEAUL).

Author information

Authors and Affiliations

  1. Département des Sciences du Bois et de la Forêt, Université Laval, Québec, QC, Canada

    Carla Francisco

  2. Departamento de Ciências e Tecnologia, Universidade Aberta, Portugal and Centro de Estatística e Aplicações, Universidade de Lisboa, Lisboa, Portugal

    Teresa A. Oliveira & Amílcar Oliveira

  3. Unidade Departamental de Matemática e Física, Instituto Politécnico de Tomar and CMA – Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal

    Francisco Carvalho

Authors
  1. Carla Francisco
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  2. Teresa A. Oliveira
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  3. Amílcar Oliveira
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  4. Francisco Carvalho
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Corresponding author

Correspondence to Carla Francisco .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Brock University, St. Catharines, ON, Canada

    S. Ejaz Ahmed

  2. Departmental Unit of Mathematics and Physics, Polytechnic Institute of Tomar, Tomar, Portugal

    Francisco Carvalho

  3. Faculty of Natural Sciences, University of Tampere, Tampere, Finland

    Simo Puntanen

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Francisco, C., Oliveira, T.A., Oliveira, A., Carvalho, F. (2019). Hadamard Matrices on Error Detection and Correction: Useful Links to BIBD. In: Ahmed, S., Carvalho, F., Puntanen, S. (eds) Matrices, Statistics and Big Data. IWMS 2016. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-17519-1_8

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