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

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.