The class of duadic codes was defined previously [V. Pless, Introduction to the theory of error correcting codes (1981; Zbl 0481.94004)] as a class of binary, cyclic \((n,(n\pm 1)/2)\) codes. Let \(\mu_ a\) denote the coordinate permutation \(i\to ai(mod n)\), \((a,n)=1\), and S the set of nonzero cyclotomic cosets for n and \(S_ 1\), \(S_ 2\) two disjoint subsets of cosets, \(S=S_ 1\cup S_ 2\), such that \(\mu_ a\) interchanges \(S_ 1\) and \(S_ 2\). Then \(S_ 1\) and \(S_ 2\) is called a splitting. A cyclic code is called duadic if its idempotent is one of \(e_ j=\sum_{i\in S_ j}x^ i\), \(j=1,2\). Such codes exist for length n iff \(n=\prod_{i}p_ i^{a_ i}\) where \(p_ i\equiv \pm 1(mod p)\) and the class includes the class of quadratic residue codes. Properties of duadic codes are investigated. Conditions are found on n under which an extended duadic code is self-dual or its dual is the other duadic code. In the self-dual case a characterization of code weights is given and the square root bound is improved. It is also shown that every extended cyclic self-dual binary code is a duadic code. Extensive tables are given describing minimum weights and the duals of all duadic codes up to length 241.