The minimum distance of cycle-free codes

The following theorem gives an upper bound on the minimum distance
of cycle-free linear codes. Later in this section, we will show
that this bound is tight for all values of *n* and *k*.

Observe that for
*k*/*n*0.5, the bound in (3.6)
reduces to *d*2. This simple special case was dealt with in Theorem 3.3.
The proof of Theorem 3.6 for general *n* and *k*
is considerably more involved and will be presented
in Section 3.4.2,
after we establish a series of auxiliary lemmas in the
next subsection.

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