Block code: Difference between revisions

Revision as of 18:22, 22 April 2018

Revision as of 18:28, 22 April 2018

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== Lower and upper bounds of block codes ==

[[File:HammingLimit.png|thumb|720px|Hamming Limitlimit]]

[[File:Linear Binary Block Codes and their needed Check Symbols.png|thumb|720px|

There are theoretical limits (such as the hammingHamming limit), but another question is which codes can actually constructed. It is like [[Sphere packing|packing spheres in a box]] in many dimensions ... This diagram shows the constructableconstructible codes, which are linear and binary. The ''x-'' axis shows the number of protected symbols ''k'', the ''y-'' axis the number of needed check symbols n-k''n–k''. Plotted are the limits for different Hamming distances from 1 (unprotected) to 34.

Marked with dots are perfect codes:

{{bulleted list

| light orange on ''x-'' axis: trivial unprotecedunprotected codes

| orange on ''y-'' axis: trivial repeat codes

| dark orange on data set ''d''{{=}}3: classic perfect hammingHamming codes

| dark red and larger: the only perfect binary Golay code

}}