  Visontai conjectured in 2013 that the joint distribution of ascent and
distinct nonzero value numbers on the set of subexcedant sequences is the same
as that of descent and inverse descent numbers on the set of permutations. This
conjecture has been proved by Aas in 2014, and the generating function of the
corresponding bistatistics is the double Eulerian polynomial. Among the
techniques used by Aas are the M\"obius inversion formula and isomorphism of
labeled rooted trees. In this paper we define a permutation code (that is, a
bijection between permutations and subexcedant sequences) and show the more
general result that two $5$-tuples of set-valued statistics on the set of
permutations and on the set of subexcedant sequences, respectively, are
equidistributed. In particular, these results give a bijective proof of
Visontai's conjecture.
