Linear Codes

Linear codes provide an optimal way for transmitting blocks of data over noisy channels

Originator: Andries E. Brouwer and Markus Grassl

(808 elements)

Examples

Basic Examples

Retrieve the default content:

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Other Examples

Show data for the Golay code (A further exploration can be found at the Wolfram Demonstration Golay Code):

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Generate a triangle of optimal distances with the blocklength (length of the codeword) on the left and the dimension (number of data bits) on the bottom:

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With[{data = ResourceData["c055e245-f65e-4a21-a807-6346617f515a"]}, Style[Text@
Grid[Append[
PadRight[Prepend[#, #[[1]]], 40, ""] & /@ Table[data[{a, b}]["Distance"], {a, 3, 40}, {b, 1, a - 1}], Join[{""}, Range[1, 39]]], Dividers -> {{2 -> True}, {39 -> True}}], 10]]

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Generate a grid of some of the optimal generator matrices:

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With[{data = ResourceData["c055e245-f65e-4a21-a807-6346617f515a"]}, Grid[Table[
ArrayPlot[data[{a, b}]["GeneratorMatrix"], PixelConstrained -> True, ImageSize -> {2 data[{a, b}]["BlockLength"] + 4, 2 data[{a, b}]["Dimension"] + 4}, Frame -> False], {a, 20, 28}, {b, 8, 16}]]]

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Bibliographic Citation

Wolfram Research, "Linear Codes" from the Wolfram Data Repository (2017) https://doi.org/10.24097/wolfram.23530.data

Data Resource History

Date Created: 10 July 2017

Source Metadata

Source: http://www.codetables.de/
Citation: Markus Grassl, “Bounds on the minimum distance of linear codes and quantum codes.”

Data Downloads

Publisher Information

Prepared for the Wolfram Data Repository By: Ed Pegg Jr
Publisher of Record: Wolfram Research