| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Research Abstract |
We define an (N,k,d) error-correcting sequence over GF(q) as a periodic sequence a_0,a_1,a_2,... of elements in GF(q) with period N, such that its sub k-tuples (a_i, a_{i+1}, ..., a_{i+k-1}) are all distinct for i=0,1,...N-1, and they form an error-correcting code with minimum distance d.
Admitting a moderate conjecture on the existence of primitive polynomials whose coeffients constitute a De Bruijn sequence or a Projective De Bruijn sequence, we prove the existence of a binary (2^{2^m-m-2}-1,2^m-2,3) error-correcting sequence and (q^{\frac{q^m-1}{q-1}-m}-1,\frac{q^m-1}{q-1},3) error-correcting sequence over GF(q).
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