Minimum-weight MIPPR word conjecture for minimal PPRIC codes

Let $r$, $s$, and $L$ be nonnegative integers with $L\geqslant 2s+r+1$, and let $C\subseteq {\cal W}_s$ be a minimal $(L,s,r)$ PPRIC code. An MIPPR word is a word associated with $C$ having the minimum possible intersection property described for PPRIC codes. Minimum-weight MIPPR word conjecture. Any MIPPR word of minimum weight in $C$ has weight $r+3$. By the preceding lemma, every MIPPR word has weight at least $r+3$; the conjecture asserts that this lower bound is attained for minimal PPRIC codes. The paper presents it as an intriguing conjecture motivating constructions and lower bounds, with no resolution given.