From: Jonas Ohlsson <jonoh@isy.liu.se>
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.