 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-2/12k/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

c \in C

had odd Hamming weight, add all

n

cyclic shifts of

c

. Each coordinate of the sum is the sum of all coordinates of

c

, namely one in

F_{2}

. Linearity and cyclicity would therefore put

(1, \dots, 1)

C

, contrary to the hypothesis. Hence every codeword has even weight.

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