R: Vectorized recoding values in one data frame based on another data frame [duplicate]

I have a data frame with a row of numbers and a row of letters. Let's call this the "decoder key." Each column in the decoder key represents a mapping between numbers and letters.

I also have a data frame with a column of codes comprised of numbers of varying digits. I want to create a new variable in this latter data frame that "translates" these codes from numbers to letters using the decoder key. In other words, I'll have the original number-based codes and then I'll have another column with the letters that correspond to that code.

I tried to implement this with a loop and dplyr::recode() but (a) I bet there's a better way to do this and (b) recode doesn't seem to work with the indexing. Any solutions? Below is a small reproducible example. In the real data, the alphas, numbers, and codes vectors are very large.

# Load packages
library(dplyr)

# Generate decoder
key <- data.frame(alphas = c("A","B","C"),
                  numbers = c("1","2","3"),
                  stringsAsFactors = FALSE)

# Generate codes from the possible values
# found in key$numbers
code_df <- data.frame(codes = c("2313","2","123","321"),
                    stringsAsFactors = FALSE)

# Add "decoded value" to the codes table by
# converting any number in a code into the letter
# found above the code in the key data.frame. Loop
# through each possible number requiring decoding
# in the decoder table and replace it with the letter
# above it
for(i in 1:ncol(key)){
  code_df$codes <- dplyr::recode(x = code_df$codes, key[2,i] = key[1,i])
  }

Note: this is different from the following posts because I need to recode the variable rather than join two variables and I also have large enough data where I cannot do this manually.

Changing value of data frame based on another data frame

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