Cyclotomy and duadic codes of prime lengths
Cunsheng Ding, Vera S. Pless · IEEE Transactions on Information Theory · 1999
We present a cyclotomic approach to the construction of all binary duadic codes of prime lengths. We calculate the number of all binary duadic codes for a given prime length and that of all duadic codes that are not quadratic residue codes. We give necessary and sufficient conditions for p such that all binary duadic codes of length p are quadratic residue (QR) codes. We also show how to determine some weights of duadic codes with the help of cyclotomic numbers.