Abstract
Since their definition in 1984 [7] there has been much work on duadic codes with generalizations in various directions. We survey this for its own interest and as it might shed light on cyclic codes in general. Duadic codes are generalizations of quadratic residue codes. This tells us for which lengths n they exist and also gives us an easy way to construct their generating idempotents over fields of characteristic 2. As cyclic codes whose extensions are self-dual must be duadic, we also learn at which lengths such codes can exist. On the one hand duadic codes are generalized to triadic and polyadic codes, and on the other hand to codes generated by difference sets in abelian groups.
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