DocumentCode :
916662
Title :
Weight distributions of the cosets of the (32,6) Reed-Muller code
Author :
Berlekamp, Elwyn R. ; Welch, Lloyd R.
Volume :
18
Issue :
1
fYear :
1972
fDate :
1/1/1972 12:00:00 AM
Firstpage :
203
Lastpage :
207
Abstract :
In this paper we present the weight distribution of all 
cosets of the (32,6) first-order Reed-Muller code. The code is invariant under the complete affine group, of order 
16. In the Appendix we show (by hand computations) that this group partitions the cosets into only 48 equivalence classes, and we obtain the number of cosets in each class. A simple computer program then enumerated the weights of the 32 vectors ih each of the 48 cosets. These coset enumerations also answer this equivalent problem: how well are the 
Boolean functions of five variables approximated by the 
linear functions and their complements?
cosets of the (32,6) first-order Reed-Muller code. The code is invariant under the complete affine group, of order 16. In the Appendix we show (by hand computations) that this group partitions the cosets into only 48 equivalence classes, and we obtain the number of cosets in each class. A simple computer program then enumerated the weights of the 32 vectors ih each of the 48 cosets. These coset enumerations also answer this equivalent problem: how well are the Boolean functions of five variables approximated by the linear functions and their complements?Keywords :
Reed-Muller codes; Boolean functions; Laboratories; Linear code; Mathematics; Telephony; Vectors;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1972.1054732
Filename :
1054732
Link To Document :
