  Independent parallel q-ary symmetric channels are a suitable transmission
model for several applications. The proposed weighted-Hamming metric is
tailored to this setting and enables optimal decoding performance. We show that
some weighted-Hamming-metric codes exhibit the unusual property that all errors
beyond half the minimum distance can be corrected. Nevertheless, a tight
relation between the error-correction capability of a code and its minimum
distance can be established. Generalizing their Hamming-metric counterparts,
upper and lower bounds on the cardinality of a code with a given
weighted-Hamming distance are obtained. Finally, we propose a simple code
construction with optimal minimum distance for specific parameters.
