A CONSTRUCTION OF F-2-LINEAR CYCLIC, MDS CODES

Author(s)

Cardell, Sara D. ^[1] ; Climent, Joan-Josep ^[2] ; Panario, Daniel ^[3] ; Stevens, Brett ^[3]

Affiliation

^[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Campinas - Brazil

^[2] Univ Alacant, Dept Matemat, Alacant - Spain

^[3] Carleton Univ, Sch Math & Stat, Ottawa, ON - Canada

• Document type: Journal article
• Source: Advances in Mathematics of Communications; v. 14, n. 3, p. 437-453, AUG 2020.
• Web of Science Citations: 0

Abstract

In this paper we construct F-2-linear codes over F-2(b) with length n and dimension n - r where n = rb. These codes have good properties, namely cyclicity, low density parity-check matrices and maximum distance separation in some cases. For the construction, we consider an odd prime p, let n = p - 1 and utilize a partition of Z(n). Then we apply a Zech logarithm to the elements of these sets and use the results to construct an index array which represents the parity-check matrix of the code. These codes are always cyclic and the density of the parity-check and the generator matrices decreases to 0 as n grows (for a fixed r). When r = 2 we prove that these codes are always maximum distance separable. For higher r some of them retain this property. (AU)

• FAPESP's process: 16/50476-0 - Efficiency and security of pre and post quantum cryptographic methods: theory and applications
• Grantee: Ricardo Dahab
• Support Opportunities: Regular Research Grants