Weight Distribution


Reed-Muller Codes

(8,4)
(16,5) (16,11)
(32,6) (32,16) (32,26)
(64,7) (64,22) (64,42) (64,57)
(128,8) (128,29) (128,64)*1 (128,99)
(256,9) (256,37) (256,93) (256,163)
(512,10) (512,46) (512,130) (512,256) (512,382)

Extended Binary Primitive BCH Codes

(8,4)
(16,5) (16,7) (16,11)
(32,6) (32,11) (32,16) (32,21) (32,26)
(64,7) (64,10) (64,16) (64,18) (64,24) (64,30) (64,36) (64,39) (64,45) (64,51) (64,57)
(128,8) (128,15) (128,22) (128,29)*3 (128,36)*3 (128,43)*3 (128,50)*3 (128,57)*3 (128,64)*3 (128,71)*3 (128,78)*3 (128,85)*3 (128,92)*3 (128,99)*3 (128,106) (128,113) (128,120)
(256,9) (256,13) (256,21) (256,29)*4 (256,37)*4 (256,45)*4 (256,47)*4 (256,55)*4 (256,63)*4 (256,71) (256,79) (256,87) (256,91) (256,99) (256,107) (256,115) (256,123) (256,131) (256,139) (256,147) (256,155) (256,163) (256,171) (256,179) (256,187) (256,191) (256,199) (256,207)*4 (256,215)*4 (256,223)*4 (256,231) (256,239) (256,247)

Binary Primitive BCH Codes

(7,4)
(15,5) (15,7) (15,11)
(31,6) (31,11) (31,16) (31,21) (31,26)
(63,7) (63,10) (63,16) (63,18) (63,24) (63,30) (63,36) (63,39) (63,45) (63,51) (63,57)
(127,8) (127,15) (127,22) (127,29) (127,36) (127,43) (127,50) (127,57) (127,64) (127,71) (127,78) (127,85) (127,92) (127,99) (127,106) (127,113) (127,120)
(255,9) (255,13) (255,21) (255,29) (255,37) (255,45) (255,47) (255,55) (255,63) (255,71) (255,79) (255,87) (255,91) (255,99) (255,107) (255,115) (255,123) (255,131) (255,139) (255,147) (255,155) (255,163) (255,171) (255,179) (255,187) (255,191) (255,199) (255,207)*4 (255,215)*4 (255,223)*4 (255,231) (255,239) (255,247)

Reference

*1 M. Sugino, Y. Tokura and T. Kasami, "Weight Distribution of (128,64) Reed-Muller Code,", IEEE Transaction on Information Theory, 17, pp.627-628, 1971
*2 T. Sugita, T. Kasami and T. Fujiwara, "The Weight Distribution of the Third -Order Reed-Muller Code of Length 512," IEEE Transaction on Information Theory, 42, 5, pp.1622-1625, September 1996
*3 Y. Desaki, T. Fujiwara and T. Kasami, "The Weight Distribution of Extended Binary Primitive BCH Code of Lenght 128," IEEE Transaction on Information Theory, 43, 4, pp.1364-1371, July. 1997
*4 T. Fujiwara and T. Kasami, "The Weight Distribution of (256,k) Extended Binary Primitive BCH Code with k <= 63, k>=207," Technical Report of IEICE, IT97-46, pp.29-33, September, 1993

Acknowledgments

We would like to thank Professors Desaki, Fujiwara and Tomita for their help to provide numerical data and useful suggestions.
Created by M. Terada, J. Asatani and T. Koumoto.