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Cyclotomy and duadic codes of prime lengths

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2 Author(s)
Cunsheng Ding ; Dept. of Comput. Sci., Univ. of Singapore, Singapore ; Pless, V.

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

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Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 2 )