Title :
Cyclic subcodes of generalized Reed-Muller codes
Author :
Moreno, O. ; Duursma, I.M. ; Cherdieu, J.-P. ; Edouard, A.
Author_Institution :
Gauss Res. Lab., Puerto Rico Univ., Rio Piedras, Puerto Rico
fDate :
1/1/1998 12:00:00 AM
Abstract :
We consider certain subcodes of generalized Reed-Muller (GRM) codes, which we call homogeneous generalized Reed-Muller (HRM) codes. In general, they have a much better minimum distance than the GRM codes. The parameters of HRM codes are related to those of projective Reed-Muller (PRM) codes. Unlike most PRM codes, punctured HRM codes are cyclic. Under the trace map, HRM codes map to binary codes. These are in general much larger than classical RM codes, for the same minimum distance
Keywords :
Reed-Muller codes; cyclic codes; polynomials; HRM codes; binary codes; cyclic subcodes; generalized Reed-Muller codes; homogeneous generalized Reed-Muller codes; minimum distance; projective Reed-Muller codes; punctured codes; Binary codes; Cryptography; Decoding; Error correction codes; Hamming distance; Hamming weight; Human resource management; Information theory; Notice of Violation; Upper bound;
Journal_Title :
Information Theory, IEEE Transactions on
