From: Jonas Ohlsson Subject: Re: weights of Reed-Muller Codes Date: 6 Apr 1999 17:00:16 -0500 Newsgroups: sci.math.research Gabriela N Stanica wrote: > Does anybody know what is the state of the art for the problem > of weight enumeration (or anything about Hamming weights) of > Reed-Muller codes? I know (MacWilliams and Sloane "The Theory of > Error-Correcting Codes" ) that in 1977 the smallest Reed-Muller > codes for which the weight distribution was not known were > R(3,9),R(4,9),R(5,9) but I suspect the situation has changed. > Thanks for any input on the problem. > > Pantelimon Stanica,Ph.D. > Department of Mathematics > State University of New York at Buffalo > Buffalo, NY 14214 > stanica@math.buffalo.edu There is a quite recent article in the journal IEEE Transactions on Information Theory on the weight distribution of R(3,9). The reference is: T. Sugita, T. Kasami, T. Fujiwara, "The weight distribution of the third-order Reed-Muller code of length 512", IT-42, no. 5, september, 1996. In the article one can also find a reference to an article where the weight distribution of R(5,9) is determined.