Year: 2021
Type: preprint
Abstract: In this work, we define three composite matrices derived from group rings. We employ these composite matrices to create generator matrices of the form [In | Ω(v)], where In is the identity matrix and Ω(v) is a composite matrix and search for binary self-dual codes with parameters [36, 18, 6 or 8]. We next lift these codes over the ring R1 = F2 + uF2 to obtain codes whose binary images are self-dual codes with parameters [72,36,12]. Many of these codes turn out to have weight enumerators with parameters that were not known in the literature before. In particular, we find 30 new Type I binary self-dual codes with parameters [72, 36, 12].
Source: arXiv (Cornell University)
Authors: Korban, Adrian, Sahinkaya, Serap, Ustun, Deniz
Institutions: University of Chester, Tarsus University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3127192053