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We prove new upper bounds on the smallest size of affine blocking sets, thatis, sets of points in a finite affine space that intersect every affinesubspace of a fixed codimension. We show an equivalence between affine blockingsets with respect to codimension-$2$ subspaces that are generated by taking aunion of lines through the origin, and strong blocking sets in thecorresponding projective space, which in turn are equivalent to minimal codes.Using this equivalence, we improve the current best upper bounds on thesmallest size of a strong blocking set in finite projective spaces over fieldsof size at least $3$. Furthermore, using coding theoretic techniques, weimprove the current best lower bounds on strong blocking set.  Over the finite field $\mathbb{F}_3$, we prove that minimal codes areequivalent to linear trifferent codes. Using this equivalence, we show that anylinear trifferent code of length $n$ has size at most $3^{n/4.55}$, improvingthe recent upper bound of Pohoata and Zakharov. Moreover, we show the existenceof linear trifferent codes of length $n$ and size at least $\frac{1}{3}\left(9/5 \right)^{n/4}$, thus (asymptotically) matching the best lower bound ontrifferent codes.  We also give explicit constructions of affine blocking sets with respect tocodimension-$2$ subspaces that are a constant factor bigger than the best knownlower bound. By restricting to $\mathbb{F}_3$, we obtain linear trifferentcodes of size at least $3^{7n/240}$, improving the current best explicitconstruction that has size $3^{n/112}$.

Blocking sets, minimal codes and trifferent codes