Evaluation of a bound by DFT for cyclic codes

概要

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The Schaub bound is one of well-known lower bounds of the minimum distance for a cyclic code, and de-fined from its defining set. In 2003, this bound was improved and an algorithm for this improved bound was given by F.Ponchio and M.Sala. We give some properties of the Schaub bound and its improvements in order to investigate a relationship with the Roos bound and the shift bound by showing many numerical examples for binary and ternary cyclic codes with short length, and search a fast algorithm for the Schaub bound and the improved Schaub bound. We claim one conjecture that the value from defining set of given cyclic code is the minimum of the values from defining set in all of its cyclic subcodes by our numerical examples. This property implies to give a fast algorithm of the Schaub bound. Moreover it is shown that there is no Schaub bound greater than both the Roos bound and the shift bound in our numerical examples.