

A322074


Maximum number of codewords a binary selfdual code of length 4n can have with Hamming weight 2n (half of length).


0




OFFSET

1,1


COMMENTS

All binary selfdual codes of length 2*18 = 36 have a(9) = 131072 or fewer codewords with Hamming weight 18. In fact, there is only one binary selfdual code of length 36 that has 131072 codewords with Hamming weight 18.
There is at least one binary selfdual code of length 4n having a(n) codewords of weight 2n. However, the code may not be unique. There are two binary selfdual codes of length 4*4=16 having a(4)=198 codewords with Hamming weight 2*4=8.
All binary selfdual 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

Table of n, a(n) for n=1..9.
W. Cary Huffman and Vera Pless, Fundamentals of Error Correcting Codes, 2003, Page 7, 252330, 338393.


CROSSREFS

Cf. A322073, A321969, A296086, A001405, A000984.
Sequence in context: A226565 A231050 A337338 * A083015 A282036 A050591
Adjacent sequences: A322071 A322072 A322073 * A322075 A322076 A322077


KEYWORD

nonn,more


AUTHOR

Nathan J. Russell, Nov 25 2018


STATUS

approved



