Reading: (from course text)

Read Sections 2.1 - 2.5 by Monday Feb 16, as well as 3.7 if you wish.

Problems:

Problem A: Let C be an [n,k,d] (binary) linear code. Prove it contains exactly 2^k codewords.

Problem B: Let U be a subspace of F_2^n. Prove its dual is a subspace.

Problem C: Let V = F_2^n. Find all vectors v such that v is orthogonal to itself. Do these form a subspace? Note that the existence of such vectors implies that in general U and its dual ("orthogonal complement") are not disjoint, unlike the case of real or complex vectorspaces.

From course text:

Section 2.1: 2.1.2, 2.1.4, 2.1.5

Section 2.4: 2.4.2, 2.4.4

Section 2.5: 2.5.4

Section 3.7: 3.7.1