Codis detectors d'errors i algunes de les seves aplicacions a la societat de la informació

Authors

  • Mercè Villanueva
  • Cristina Fernández-Córdoba

Abstract

In digital transmissions of information from a sender to a receiver through a channel, errors may occur. In this article, the most important concepts and results of the theory of error detecting and correcting codes are discussed. This theory studies efficient methods to guarantee accurate transmission of information. First, some everyday examples of error detecting codes are described, such as the codes included in DNI, ISBN, IBAN and EAN. Next, the classical theory of error correcting codes is presented, particularly considering linear codes and, within them, cyclic codes, which are more efficient for encoding. The two most important families of cyclic codes, the BCH and Reed-Solomon codes, which also make it possible to decode efficiently, are also described. Lastly, two historical applications, in computer memories and the transmission of photographs in space, and two more recent applications, in QR codes and distributed storage, are shown.

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Published

2019-07-23

How to Cite

Villanueva, M., & Fernández-Córdoba, C. (2019). Codis detectors d’errors i algunes de les seves aplicacions a la societat de la informació. Butlletí De La Societat Catalana De Matemàtiques, 34(1), 53–89. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/104070.003

Issue

Vol. 34 No. 1 (2019)

Section

Articles

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