  In this paper, we consider weighted nonbinary repeat multiple-accumulate
(WNRMA) code ensembles obtained from the serial concatenation of a nonbinary
rate-1/n repeat code and the cascade of L>= 1 accumulators, where each encoder
is followed by a nonbinary random weighter. The WNRMA codes are assumed to be
iteratively decoded using the turbo principle with maximum a posteriori
constituent decoders. We derive the exact weight enumerator of nonbinary
accumulators and subsequently give the weight enumerators for WNRMA code
ensembles. We formally prove that the symbol-wise minimum distance of WNRMA
code ensembles asymptotically grows linearly with the block length when L >= 3
and n >= 2, and L=2 and n >= 3, for all powers of primes q >= 3 considered,
where q is the field size. Thus, WNRMA code ensembles are asymptotically good
for these parameters. We also give iterative decoding thresholds, computed by
an extrinsic information transfer chart analysis, on the q-ary symmetric
channel to show the convergence properties. Finally, we consider the binary
image of WNRMA code ensembles and compare the asymptotic minimum distance
growth rates with those of binary repeat multiple-accumulate code ensembles.
