I don't quite get that paper, but it mentions Conway's book On Numbers and Games, presumably for his proof that "a suitable beginnjbg segment of On_2 is an algebraic closure of the two-element subfield {0,1}".

I suppose it's not where he wrote about his notation for GF(2^n), or maybe it is. Many years ago I flipped through On Numbers and Games, but I wasn't ready then. Maybe I am now.

Anyways, Richard A. Parker seems to have put Conway's compatibility criterion into a full definition and himself named the resulting polynomials after Conway. I haven't found where Parker published about this. I'm not very good at finding publications, what do people use to find stuff? Google Scholar?

nostr:npub1knzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqpac73p