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The class of k-bit delay decodable codes, source codes allowing decoding delay of at most k bits for k ≥ 0, can attain a shorter average codeword length than Huffman codes. This paper discusses the general properties of the class of k-bit delay decodable codes with a finite number of code tables and proves two theorems which enable us to limit the scope of code-tuples to be considered when discussing optimal k-bit delay decodable code-tuples.