Galois-field Kingdom

In Galois fields, full of flowers
primitive elements dance for hours
climbing sequentially through the trees
and shouting occasional parities
 
The syndromes like ghosts in the misty damp
feed the smoldering fires of the Berlekamp
and high-flying exponents sometimes are downed
on the jagged peaks of the Gilbert bound.

S. B. Weinstein

The Galois-field Kingdom lies in the Classical Domain.

Root codes of the Galois-field Kingdom:

  • \(q\)-ary code (127 codes)
  • Convolutional code (4 codes)
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Classical Domain

  • Binary Kingdom
  • Galois-field Kingdom
  • Matrix Kingdom
  • Analog Kingdom
  • Spherical Kingdom
  • Ring Kingdom
  • Group Kingdom
  • Homogeneous-space Kingdom

Quantum Domain

  • Qubit Kingdom
  • Modular-qudit Kingdom
  • Galois-qudit Kingdom
  • Bosonic Kingdom
  • Spin Kingdom
  • Group quantum Kingdom
  • Homogeneous-space quantum Kingdom
  • Category Kingdom

Classical-quantum Domain

  • Binary c-q Kingdom
  • Analog c-q Kingdom

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Error correction zoo by Victor V. Albert, Philippe Faist, and many contributors. This work is licensed under a CC-BY-SA License. See how to contribute.