11 citations · 40 across the 15 of their papers we have counts for
16 papers
Lower and Upper Lie Nilpotency Indices of Modular Group Algebras
Joe Gildea
We resolve the remaining cases of a longstanding problem on the lower and upper Lie nilpotency indices of modular group algebras. Equality of the two indices has been known in char…
Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours
Joe Gildea, Adrian Korban, Adam Michael Roberts +1
In this work, we define a modification of a bordered construction for self-dual codes which utilises -circulant matrices. We provide the necessary conditions for the constructio…
Group LCD and Group Reversible LCD Codes
Steven T. Dougherty, Joe Gildea, Adrian Korban +1
In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the matrices…
New binary self-dual codes of lengths 56, 62, 78, 92 and 94 from a bordered construction
Joe Gildea, Adrian Korban, Adam Michael Roberts +1
In this paper, we present a new bordered construction for self-dual codes which employs -circulant matrices. We give the necessary conditions for our construction to produce sel…
New binary self-dual codes of lengths 80, 84 and 96 from composite matrices
Joe Gildea, Adrian Korban, Adam Michael Roberts
In this work, we apply the idea of composite matrices arising from group rings to derive a number of different techniques for constructing self-dual codes over finite commutative F…
New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction
Joe Gildea, Adrian Korban, Adam Michael Roberts
In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using -circulant matrices. The new construction was derived as a modifica…