File:Linear Binary Block Codes and their needed Check Symbols.png

Summary

Description
English: Linear Binary Block Codes.

There theoretical limits (such as the hamming limit), but another question is which codes can actually be constructed. It is like putting spheres in a box ... This diagram shows the constructable 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. Plotted are the limits for different Hamming distances from 1 (unprotected) to 34. Marked with dots are perfect codes:

  • light orange: trivial unprotected codes
  • orange: trivial repeat codes
  • dark orange: classic perfect hamming codes
  • red: the only perfect binary Golay code
Date
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Author Frank Klemm

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Category:Self-published work Category:Information theory Category:Coding Category:Computer programming
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