11 citations · 40 across the 15 of their papers we have counts for
5 papers · 1 filter
New Extremal Binary Self-Dual Codes from Block Circulant Matrices and Block Quadratic Residue Circulant Matrices
Joe Gildea, Abidin Kaya, Rhian Taylor +2
In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions wh…
New Self-Dual Codes of length 68 from a 2 by 2 block matrix Construction and Group Rings
Maria Bortos, Joe Gildea, Abidin Kaya +2
Many generator matrices for constructing extremal binary self-dual codes of different lengths have the form G=(I|A), where I is the n by n identity matrix and A is the n by n matri…
Composite Matrices from Group Rings, Composite G-Codes and Constructions of Self-Dual Codes
Steven T. Dougherty, Joe Gildea, Adrian Korban +1
In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ri…
New Extremal binary self-dual codes of length 68 from a novel approach to neighbors
Joe Gildea, Abidin Kaya, Adrian Korban +1
In this work, we introduce the concept of distance between self-dual codes, which generalizes the concept of a neighbor for self-dual codes. Using the k-neighbors, we are able to c…
New Self-Dual Codes from 2x2 Block Circulant Matrices, Group Rings and Neighbours of Neighbours
Joe Gildea, Abidin Kaya, Rhian Taylor +1
In this paper, we construct self-dual codes from a construction that involves 2x2 block circulant matrices, group rings and a reverse circulant matrix. We provide conditions whereb…