# OK to post
# HW4, Robert Dougherty-Bliss, 2024-02-01

# 3.

read "C4.txt":

K := 1000:

# this takes a while to run.
get_max_sizes := proc(K, attempts):
    max_sizes := table():
    for d in [3, 5, 7] do
    for n from 5 to 16 do
        max_size := -1:
        best_code := NULL:

        for attempt from 1 to attempts do
            code := RC(2, n, d, K):
            if nops(code) > max_size then
                max_size := nops(code):
                best_code := code:
            fi:
        od:

        max_sizes[(d, n)] := max_size:
    od:
    od:

    op(max_sizes):
end:

# 4.

# A perfect code matches the sphere packing bound. So, any perfect (2, n, 3)
# code must have

#   2^n / (1 + n).

# In this case, with n = 2^r - 1, we have

#   2^(2^r - r - 1)

# codewords.