Binary even [25,15,6] codes do not exist (Corresp.)

That binary even <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[25,15,6]</tex> codes do not exist is proved by passing from coding theory to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{ F}₂</tex> -affine geometry; all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">25</tex> -sets in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{ F}⁹₂</tex> are shown to contain affine planes.