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 (121 codes)
• Convolutional code (4 codes)
• Poset code (3 codes)