Information on Result #813353
Linear OOA(3100, 9846, F3, 2, 17) (dual of [(9846, 2), 19592, 18]-NRT-code), using OOA 2-folding based on linear OA(3100, 19692, F3, 17) (dual of [19692, 19592, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3100, 19683, F3, 17) (dual of [19683, 19583, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(391, 19683, F3, 16) (dual of [19683, 19592, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3102, 9847, F3, 2, 17) (dual of [(9847, 2), 19592, 18]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3101, 9846, F3, 2, 17) (dual of [(9846, 2), 19591, 18]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3100, 6598, F3, 3, 17) (dual of [(6598, 3), 19694, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3100, 6598, F3, 4, 17) (dual of [(6598, 4), 26292, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(3100, 6598, F3, 5, 17) (dual of [(6598, 5), 32890, 18]-NRT-code) | [i] | ||
| 6 | Digital (83, 100, 6598)-net over F3 | [i] | ||