Information on Result #1022540
Linear OOA(8116, large, F81, 3, 4), using generalized (u, u+v)-construction based on
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(810, s, F81, 3, 0) for arbitrarily large s, using
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(810, 265722, F81, 3, 0) (dual of [(265722, 3), 797166, 1]-NRT-code) (see above)
- linear OOA(811, 265722, F81, 3, 1) (dual of [(265722, 3), 797165, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 3, 1) for arbitrarily large s, using
- linear OOA(811, 265722, F81, 3, 1) (dual of [(265722, 3), 797165, 2]-NRT-code) (see above)
- linear OOA(814, 265722, F81, 3, 2) (dual of [(265722, 3), 797162, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(814, 538084, F81, 3, 2) (dual of [(538084, 3), 1614248, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(814, 538084, F81, 2, 2) (dual of [(538084, 2), 1076164, 3]-NRT-code), using
- appending kth column [i] based on linear OA(814, 538084, F81, 2) (dual of [538084, 538080, 3]-code), using
- Hamming code H(4,81) [i]
- appending kth column [i] based on linear OA(814, 538084, F81, 2) (dual of [538084, 538080, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(814, 538084, F81, 2, 2) (dual of [(538084, 2), 1076164, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(814, 538084, F81, 3, 2) (dual of [(538084, 3), 1614248, 3]-NRT-code), using
- linear OOA(8110, 265722, F81, 3, 4) (dual of [(265722, 3), 797156, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8110, 531444, F81, 4) (dual of [531444, 531434, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(817, 531441, F81, 3) (dual of [531441, 531434, 4]-code or 531441-cap in PG(6,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- OA 2-folding and stacking [i] based on linear OA(8110, 531444, F81, 4) (dual of [531444, 531434, 5]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m 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(8116, large, F81, 3, 3) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(8119, large, F81, 3, 4) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(8125, large, F81, 3, 4) | [i] | ||
| 4 | Linear OOA(8128, large, F81, 3, 4) | [i] | ||
| 5 | Linear OOA(8131, large, F81, 3, 4) | [i] | ||
| 6 | Linear OOA(8134, large, F81, 3, 4) | [i] | ||
| 7 | Linear OOA(8137, large, F81, 3, 4) | [i] | ||
| 8 | Linear OOA(8140, large, F81, 3, 4) | [i] | ||
| 9 | Linear OOA(8143, large, F81, 3, 4) | [i] | ||
| 10 | Linear OOA(8146, large, F81, 3, 4) | [i] | ||
| 11 | Linear OOA(8149, large, F81, 3, 4) | [i] | ||
| 12 | Linear OOA(8152, large, F81, 3, 4) | [i] | ||
| 13 | Linear OOA(8158, large, F81, 3, 4) | [i] | ||
| 14 | Linear OOA(8161, large, F81, 3, 4) | [i] | ||
| 15 | Linear OOA(8167, large, F81, 3, 4) | [i] | ||
| 16 | Linear OOA(8170, large, F81, 3, 4) | [i] | ||
| 17 | Linear OOA(8173, large, F81, 3, 4) | [i] | ||
| 18 | Linear OOA(8176, large, F81, 3, 4) | [i] | ||
| 19 | Linear OOA(8182, large, F81, 3, 4) | [i] | ||
| 20 | Linear OOA(8117, large, F81, 3, 4) | [i] | OOA Duplication | |
| 21 | Linear OOA(8116, large, F81, 4, 4) | [i] | Appending kth Column | |