Playground

Singer construction stepper

Singer's construction for a prime power q: build GF(q³) from a primitive cubic over GF(q), and for each i from 0 to v − 1 = q² + q compute the trace Tr(αⁱ) = αⁱ + α^(iq) + α^(iq²). The exponents with trace 0 form a (q² + q + 1, q + 1, 1) difference set D. Step through it, play it, or jump to the end to see every difference checked. The address bar keeps q and the step, so you can share a view.

Background: Lesson 12 (the Singer numbering),Lesson 13 (the Singer cycle), andLesson 14 (the trace construction).