| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Outline of Final Research Achievements |
We define an (N,k,d) error-correcting sequence over X as a periodic sequence {a_i}_{i=0,1,\ldots} (a_i \in X) with period N, such that its sub k-tuples {(a_i, a_{i+1}, \ldots, a_{i+k-1})|i=0,1,\ldots, N-1} (multiset) are all distinct for 0 \leq i \leq N-1, and that they form an error-correcting code with minimum distance d:= \min_{0 \leq s<t \leq N-1}{\sum_{i=0,1,2,...,k-1}\delta(a_{i+s},a_{i+t})}, where \delta(x,y)=1 for x \neq y and =0 for x=y. If d \geq 2e+1, then one can correct up to e errors in a k-tuple, so the sequence is said to be e-error correcting.
An m-sequence over GF(q) of period {q to the n} -1 is a ({q to the n}-1,n,1) error-correcting sequence. We considered when an m-sequence will be an error-correcting sequencewith minimum distance d=3 or d=5 and we gave some new constructions of error-correcting sequences.
|
