Information on Result #1018444
Linear OOA(8123, 183710, F81, 3, 7) (dual of [(183710, 3), 551107, 8]-NRT-code), using (u, u+v)-construction based on
- linear OOA(814, 6562, F81, 3, 3) (dual of [(6562, 3), 19682, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(814, 6562, F81, 2, 3) (dual of [(6562, 2), 13120, 4]-NRT-code), using
- linear OOA(8119, 177148, F81, 3, 7) (dual of [(177148, 3), 531425, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 3-folding [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), 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(8176, 2979911, F81, 3, 14) (dual of [(2979911, 3), 8939657, 15]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8180, 2979911, F81, 3, 15) (dual of [(2979911, 3), 8939653, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(8123, 183709, F81, 4, 7) (dual of [(183709, 4), 734813, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 4 | Linear OOA(8123, 183709, F81, 9, 7) (dual of [(183709, 9), 1653358, 8]-NRT-code) | [i] | ||