Two-Weight Codes, Graphs and Orthogonal Arrays
|Title:||Two-Weight Codes, Graphs and Orthogonal Arrays||Authors:||Byrne, Eimear
|Permanent link:||http://hdl.handle.net/10197/6304||Date:||2015||Abstract:||We investigate properties of two-weight codes over finite Frobenius rings, giving constructions for the modular case. A δ-modular code  is characterized as having a generator matrix where each column g appears with multiplicity δ|gR×| for some δ ∈ Q. Generalizing  and , we show that the additive group of a two-weight code satisfying certain constraint equations (and in particular a modular code) has a strongly regular Cayley graph and derive existence conditions on its parameters. We provide a construction for an infinite family of modular two-weight codes arising from unions of submodules with pairwise trivial intersection. The corresponding strongly regular graphs are isomorphic to graphs from orthogonal arrays.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||Springer||Copyright (published version):||2015 Springer||Keywords:||Codes over rings;Finite Frobenius ring;Orthogonal array;Strongly regular graph;Two-weight code;Homogeneous weight;Modular codes;Ring-linear code||DOI:||10.1007/s10623-015-0042-1||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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