BCK-codes Based on a Parity Check Matrix

• Autorzy: Keshavarzian Nazanin , Borumand Saeid Arsham , Tehranian Abolfazl

Identyfikatory

DOI

10.3233/FI-2020-1936

• Języki publikacji: EN

Abstrakty

EN

Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks.

Słowa kluczowe

EN

algorithm; atom; BCI-algebra; BCK-algebra; BCK-incidence vector; binary code; error detecting; generator matrix; Hamming distance; incidence structure; linear code; orthogonal code; parity check matrix

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2020
• Tom: Vol. 174, nr 2
• Strony: 137--165
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Keshavarzian Nazanin

• Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran

autor

Borumand Saeid Arsham

• Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

autor

Tehranian Abolfazl

• Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).