Two-Weight Codes, Graphs and Orthogonal Arrays

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Title: Two-Weight Codes, Graphs and Orthogonal Arrays
Authors: Byrne, Eimear
Sneyd, Alison
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Date: 2015
Abstract: We investigate properties of two-weight codes over finite Frobenius rings, giving constructions for the modular case. A δ-modular code [15] is characterized as having a generator matrix where each column g appears with multiplicity δ|gR×| for some δ ∈ Q. Generalizing [10] and [5], 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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