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Two-Weight Codes, Graphs and Orthogonal Arrays
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| File | Description | Size | Format | |
|---|---|---|---|---|
| byrne_sneyd_dcc.pdf | 335.34 kB | Adobe PDF | Download |
| Title: | Two-Weight Codes, Graphs and Orthogonal Arrays | Authors: | Byrne, Eimear Sneyd, Alison |
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 [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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