Two-Weight Codes, Graphs and Orthogonal Arrays
|Title:||Two-Weight Codes, Graphs and Orthogonal Arrays||Authors:||Byrne, Eimear; Sneyd, Alison||Permanent link:||http://hdl.handle.net/10197/6304||Date:||2015||Online since:||2016-01-16T04:00:18Z||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||Journal:||Designs Codes and Cryptography||Volume:||79||Issue:||2||Start page:||201||End page:||217||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||This item is made available under a Creative Commons License:||https://creativecommons.org/licenses/by-nc-nd/3.0/ie/|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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