El mètode de les línies per a la resolució numèrica d'equacions en derivades parcials Authors Cristina Dalfó Miquel A. Fiol 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. Downloads Text complet (Català) Published 2019-07-23 How to Cite Dalfó, C., & Fiol, M. A. (2019). El mètode de les línies per a la resolució numèrica d’equacions en derivades parcials. Butlletí De La Societat Catalana De Matemàtiques, 34(1), 33–51. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/104069.003 More Citation Formats ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Download Citation Endnote/Zotero/Mendeley (RIS) BibTeX Issue Vol. 34 No. 1 (2019) Section Articles License The intellectual property of articles belongs to the respective authors.On submitting articles for publication to the journal Butlletí de la Societat Catalana de Matemàtiques, authors accept the following terms:Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Butlletí de la Societat Catalana de Matemàtiques.Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.The journal Butlletí de la Societat Catalana de Matemàtiques is not responsible for the ideas and opinions expressed by the authors of the published articles.