| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Research Abstract |
This project dealt with a generalization of the theory of zeta functions for linear codes. We extended the consideration to all the polynomials which were invariant under the MacWilliams transform. Moreover we introduced a method to produce many invariant polynomials systematically from the existing codes which were not self-dual. Using this method, we considered the Riemann hypothesis for invariant polynomials which were obtained from some famous families of linear codes. They were the MDS codes, general Hamming codes and non-self-dual Golay codes. Some of them form a family "perfect codes". We could prove that, except for some sequences of the general Hamming codes, their invariant polynomials satisfied the Riemann hypothesis.
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