On Category of Linear Codes

N. Keshavarzian, A. Borumand Saeid () and A. Tehranian ()
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N. Keshavarzian: Department of Mathematics, Science and Research Branch, Islamic, Azad University (IAU), Tehran, Iran
A. Borumand Saeid: ��Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid, Bahonar University of Kerman, Kerman, Iran
A. Tehranian: Department of Mathematics, Science and Research Branch, Islamic, Azad University (IAU), Tehran, Iran

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 03, 871-887

Abstract: Recently, a number of researches studied relationship between codes and BCK-algebras, dealing with the category codes in a BCK-algebra have not been considered in earlier works. This paper investigates a code constructed by a BCK-algebra and also a BCK-algebra constructed based on code. The suggested rendered algorithm constructs the code based on BCK-algebra, the fixed dimension of this code is guaranteed by a BCK-algebra with some condition. We introduce the category of linear codes and denoted by LC. In addition, a subcategory of BCK-algebra is described and denoted by EBCK. Finally, we prove that LC is equivalent to EBCK.

Keywords: BCK-algebra; linear code; BCK-truth vector; LC category; EBCK category (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500417

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