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Two-Weight Codes, Graphs and Orthogonal Arrays
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| 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 [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 | 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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