New singly and doubly even binary [72,36,12] self-dual codes from M 2(R)G - group matrix rings
Abstract
In this work, we present a number of generator matrices of the form [ I 2 n | τ 2 ( v ) ] , where I 2 n is the 2 n × 2 n identity matrix, v is an element in the group matrix ring M 2 ( R ) G and where R is a finite commutative Frobenius ring and G is a finite group of order 18. We employ these generator matrices and search for binary [ 72 , 36 , 12 ] self-dual codes directly over the finite field F 2 . As a result, we find 134 Type I and 1 Type II codes of this length, with parameters in their weight enumerators that were not known in the literature before. We tabulate all of our findings.Citation
Korban, A., Şahinkaya, S., & Ustun, D. (2021). New singly and doubly even binary [72,36,12] self-dual codes from M2(R)G - group matrix rings. Finite Fields and their Applications, 76, Article 101924. https://doi.org/10.1016/j.ffa.2021.101924Publisher
ElsevierType
articleDescription
From Elsevier via Jisc Publications RouterHistory: accepted 2021-08-26, epub 2021-09-17, issued 2021-12-31
Article version: AM
Publication status: Published