Information on Result #1084753
Linear OOA(8129, large, F81, 4, 6), using generalized (u, u+v)-construction based on
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(810, s, F81, 4, 0) for arbitrarily large s, using
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(810, 177148, F81, 4, 0) (dual of [(177148, 4), 708592, 1]-NRT-code) (see above)
- linear OOA(811, 177148, F81, 4, 1) (dual of [(177148, 4), 708591, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(811, s, F81, 4, 1) for arbitrarily large s, using
- appending 3 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, 4, 1) for arbitrarily large s, using
- linear OOA(811, 177148, F81, 4, 1) (dual of [(177148, 4), 708591, 2]-NRT-code) (see above)
- linear OOA(811, 177148, F81, 4, 1) (dual of [(177148, 4), 708591, 2]-NRT-code) (see above)
- linear OOA(814, 177148, F81, 4, 2) (dual of [(177148, 4), 708588, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(814, 538084, F81, 4, 2) (dual of [(538084, 4), 2152332, 3]-NRT-code), using
- appending 2 arbitrary columns [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 2 arbitrary columns [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, 4, 2) (dual of [(538084, 4), 2152332, 3]-NRT-code), using
- linear OOA(816, 177148, F81, 4, 3) (dual of [(177148, 4), 708586, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(816, 538248, F81, 4, 3) (dual of [(538248, 4), 2152986, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(816, 538248, F81, 3, 3) (dual of [(538248, 3), 1614738, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(816, 538248, F81, 2, 3) (dual of [(538248, 2), 1076490, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(816, 538248, F81, 3, 3) (dual of [(538248, 3), 1614738, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(816, 538248, F81, 4, 3) (dual of [(538248, 4), 2152986, 4]-NRT-code), using
- linear OOA(8116, 177148, F81, 4, 6) (dual of [(177148, 4), 708576, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- 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(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-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(8129, large, F81, 4, 5) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(8129, large, F81, 4, 4) | [i] | ||
| 3 | Linear OOA(8129, large, F81, 4, 3) | [i] | ||
| 4 | Linear OOA(8137, large, F81, 4, 6) | [i] | NRT-Code Embedding in Larger Space | |
| 5 | Linear OOA(8141, large, F81, 4, 6) | [i] | ||
| 6 | Linear OOA(8145, large, F81, 4, 6) | [i] | ||
| 7 | Linear OOA(8149, large, F81, 4, 6) | [i] | ||
| 8 | Linear OOA(8153, large, F81, 4, 6) | [i] | ||
| 9 | Linear OOA(8165, large, F81, 4, 6) | [i] | ||
| 10 | Linear OOA(8169, large, F81, 4, 6) | [i] | ||
| 11 | Linear OOA(8181, large, F81, 4, 6) | [i] | ||
| 12 | Linear OOA(8130, large, F81, 4, 6) | [i] | OOA Duplication | |
| 13 | Linear OOA(8131, large, F81, 4, 6) | [i] | ||