Title :
Cyclotomy and duadic codes of prime lengths
Author :
Ding, Cunsheng ; Pless, Vera
Author_Institution :
Dept. of Comput. Sci., Univ. of Singapore, Singapore
fDate :
3/1/1999 12:00:00 AM
Abstract :
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
Keywords :
binary codes; cyclic codes; dual codes; residue codes; binary duadic codes; code weights; cyclic codes; cyclotomic numbers; dual codes; necessary conditions; prime lengths; quadratic residue codes; sufficient conditions; Binary codes; Computer science; Mathematics; Statistics; Sufficient conditions;
Journal_Title :
Information Theory, IEEE Transactions on
