Does There exist a [72,36,16] Type II Code?




Defintions
Weight Enumerator of a putative [72,36,16] code
Weight Enumerator of a putative [70,35,14] code
Weight Enumerator of a related length 68 code
Higher Weight Enumerator of a [72,36,16] code
Automorphism Group
Related Theorem
Other Math Sites

 

 

 
     

 

 

Does there exist a [72,36,16] Type II code?


The purpose of this page is to bring together information on this interesting open problem. The question of the existence of a [72,36,16] Type II code is the first open case in a series of questions:


Does there exist a [24k,12k,4k+4] Type II code?


For k=1 there is the extended Golay code and for k=2 there is the Quadratic Residue code. For large enough k it is known that there are no codes.



Monetary Prizes

The following monetary prizes were announced at the Yamagata conference, October, 2000 and at WCC2001 in Paris.


  • The first person who proves the existence of a Type II [72,36,16] code receives 100 American dollars (payable by S.T. Dougherty).


  • The first person who proves the non-existence of a Type II [72,36,16] code receives 200 American dollars (payable by Masaaki Harada).


    • Additionally Neil Sloane offered $10 for the solution in his original paper on the topic.


The usual conditions apply, that is the prize is awarded only once and the result must be published in a refereed reputable mathematics journal. All decisions about the prize are decided by those offering the prize.


Click here to download a .pdf file containing some details about these codes.




Thanks to Vassil Yorgov for sending information for this page.



Comments or Questions can be emailed to me.