  APN functions play a big role as primitives in symmetric cryptography as
building blocks that yield optimal resistance to differential attacks. In this
note, we consider a recent extension of a biprojective APN family by
G\"olo\u{g}lu defined on $\mathbb{F}_{2^{2m}}$. We show that this
generalization yields functions equivalent to G\"olo\u{g}lu's original family
if $3\nmid m$. If $3|m$ we show exactly how many inequivalent APN functions
this new family contains. We also show that the family has the minimal image
set size for an APN function and determine its Walsh spectrum, hereby settling
some open problems. In our proofs, we leverage a group theoretic technique
recently developed by G\"olo\u{g}lu and the author in conjunction with a group
action on the set of projective polynomials.
