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

Determine whether an extremal Type II binary self-dual code with parameters [72,36,16] exists.

self-dual codesbinary codesextremal codes

The problem

Determine whether an extremal Type II binary self-dual code with parameters [72,36,16] exists.

Date noteThe larger existence and nonexistence rewards were announced in 2000–2001.

Open since1973original Sloane offer

Last checked2026.07.27Catalog verification

Offer 01$100 · existenceSteven T. Dougherty

Personal offer

Paid once to the first solver after publication in a refereed reputable mathematics journal; the sponsors decide eligibility.

Offer 02$200 · nonexistenceMasaaki Harada

Personal offer

Paid once to the first solver after publication in a refereed reputable mathematics journal; the sponsors decide eligibility.

Offer 03$10 · either resolutionNeil Sloane

Personal offer

The sponsor page records Sloane’s standing $10 offer for either a proof or disproof.

1 unique reference linksCurrent sponsor page