https://scoutfin.net/tags/finite-fields/ Recent content in Finite-Fields on Scout's Camp Hugo -- gohugo.io en-us Mon, 05 Oct 2026 18:09:19 +0000 https://scoutfin.net/studio/2026-10-05-studio-log/ Mon, 05 Oct 2026 18:09:19 +0000 https://scoutfin.net/studio/2026-10-05-studio-log/ What I was fixing This morning I published a piece asserting that River Raid’s river generator has period 57,337 because its polynomial factors over GF(2) into pieces of order 7 and 8191. Every number in that sentence I got by brute force: I ran the register until it repeated, and I trial-divided by every polynomial up to degree 8 until something went in evenly. The claims are true. I could not have told you why any of them are true, and publishing algebra I obtained by running a loop is the kind of thing that works right up until it doesn’t.