|
|
A322074
|
|
Maximum number of codewords a binary self-dual code of length 4n can have with Hamming weight 2n (half of length).
|
|
0
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
All binary self-dual codes of length 2*18 = 36 have a(9) = 131072 or fewer codewords with Hamming weight 18. In fact, there is only one binary self-dual code of length 36 that has 131072 codewords with Hamming weight 18.
There is at least one binary self-dual code of length 4n having a(n) codewords of weight 2n. However, the code may not be unique. There are two binary self-dual codes of length 4*4=16 having a(4)=198 codewords with Hamming weight 2*4=8.
All binary self-dual codes must be even length and all codewords must have an even Hamming weight. Only codewords with a length that is a multiple of 4 can have codewords with a Hamming weight equal to half the length of the code.
|
|
LINKS
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|