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.
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.