Determination of the Goodness of Bounds on the Size of Codes

摘要

The extensive use of codes in representing messages necessitates the construction of good codes. The number of codewords which means the size of a code is the measure of the efficiency of the code and the value of the size is expected to have as large as possible. However, there should be a restriction on the size of codes so as to have a hope that there exist some good codes. The "bound on the size of codes" is the blanket name thrown over such restriction in varied forms. To date, little performance data exist to aid in the decision of which bound provides the best result for a given code. This paper aims at providing a remedy to this situation. We present several upper and lower bounds on the number of codewords in a linear or nonlinear code given the length and minimum distance of the code and provide a comprehensive comparison of them to take a closer look at their goodness. Two different approaches have been devised to carry out the whole comparison.