A mΘ spectrum of Reed-Muller codes. (18th August 2022)

• Record Type: Journal Article
• Authors: Armand, Tsimi Jean; Cedric, Pemha Binyam Gabriel
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 25:Number 6(2022)
• Page Start: 1791
• Page End: 1807
• Publication Date: 2022-08-18
• Subjects: 94B60 -- 94B75; Modal Θ valent set -- Modal Θ valent codes -- Functions of modal Θ-valent real variable (fmΘrv) -- mΘ spectrum of Reed-Muller code -- mΘ ring -- mΘ field -- mΘ vector spaces -- mΘ distance -- mΘ Boolean function -- mΘ spectrum of a Boolean algebra -- mΘ bar product; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2020.1814489
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: In this paper, we construct m Θ spectrum of Reed Muller codes, a family of m Θ linear codes [5] with large m Θ minimum distance. First, we cover the necessary material on the m Θ Boolean algebra. We then define the m Θ spectrum of Reed Muller codes RM Θ ( r, m ) as certain subspaces of the m Θ Boolean algebra . We determinate the parameters of RM Θ ( r, m ).