1. A non-transitory computer-readable recording medium having stored therein an encoding program that causes a computer to execute a process comprising: first encoding a first character string in input data to a first code, when the first character string being registered in a first dictionary, the first code being associated with the first character string in the first dictionary; second encoding a second character string in input data to a second code and registering the second character string to a dynamic dictionary, when the second character string being not registered in the first dictionary, the second code being associated with the second character string and preliminary information in the dynamic dictionary; and generating encoded data including the encoded input data and the dynamic dictionary.