Shortest synchronizing codewords of a binary Huffman equivalent code

The inherent problem of a variable-length code is that even a single bit error can cause loss of synchronization and may lead to error propagation. Synchronizing codewords have been extensively studies as a mean to overcome the drawback and efficiently stop error propagation. First we prove the restatement of a result originally given by B. Ruder (1971) in a more straightforward way. Next, we present the necessary conditions for the existence of a binary Huffman equivalent code with shortest synchronizing codeword(s). Finally, with the help of derived conditional equations, a unified approach for constructing a binary Huffman equivalent code with most shortest synchronizing codeword(s) and most other synchronizing codewords is proposed also.