Part V · Singer's algorithm · Lesson 14

Writing down a difference set

The trace-zero line gives a Singer set directly, with no search.

This lesson is planned. Here is what it will cover.

You’ll learn

• The trace $\mathrm{Tr}(x) = x + x^q + x^{q^2}$ and the trace-zero plane.
• $D = \{\, i \bmod v : \mathrm{Tr}(\alpha^i) = 0 \,\}$.
• Stepping through $q = 2, 3, 4$; $v$ field multiplications versus the brute-force count from Lesson 1.