Reading: (from course text)

Read Sections 3.1 through 3.4 up to Orthogonal Arrays, and Chapter 4 up to Latin Squares and OA Codes.

Problems:

From course text:

Section 3.1: 3.1.2, 3.1.3, 3.1.4

Section 3.2: 3.2.1, 3.2.2 (write down a multiplication table), 3.2.3 (explain your answer), 3.2.4, 3.2.5 (i.e. construct via our polynomial method), 3.2.7, 3.2.10, 3.2.11, 3.2.13

Problem A: Show there is a polynomial f(X) over F_q of degree q+1 such that f(x) = 0 for all x in F_q.

Bonus: Let f(X) be a polynomial over F_q of degree at most q-1. Show that f(x) is not 0 for all x in F_q unless f is the zero polynomial.