Information on Result #1013659
Linear OOA(743, large, F7, 3, 5), using (u, u+v)-construction based on
- linear OOA(79, 6725601, F7, 3, 2) (dual of [(6725601, 3), 20176794, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(79, 6725601, F7, 2, 2) (dual of [(6725601, 2), 13451193, 3]-NRT-code), using
- appending kth column [i] based on linear OA(79, 6725601, F7, 2) (dual of [6725601, 6725592, 3]-code), using
- Hamming code H(9,7) [i]
- appending kth column [i] based on linear OA(79, 6725601, F7, 2) (dual of [6725601, 6725592, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(79, 6725601, F7, 2, 2) (dual of [(6725601, 2), 13451193, 3]-NRT-code), using
- linear OOA(734, 5764804, F7, 3, 5) (dual of [(5764804, 3), 17294378, 6]-NRT-code), using
- trace code [i] based on linear OOA(4917, 2882402, F49, 3, 5) (dual of [(2882402, 3), 8647189, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(4917, 5764805, F49, 5) (dual of [5764805, 5764788, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(4917, 5764801, F49, 5) (dual of [5764801, 5764784, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(4917, 5764805, F49, 5) (dual of [5764805, 5764788, 6]-code), using
- trace code [i] based on linear OOA(4917, 2882402, F49, 3, 5) (dual of [(2882402, 3), 8647189, 6]-NRT-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(743, large, F7, 3, 4) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(743, large, F7, 3, 3) | [i] | ||
| 3 | Linear OOA(746, large, F7, 3, 5) | [i] | NRT-Code Embedding in Larger Space | |
| 4 | Linear OOA(749, large, F7, 3, 5) | [i] | ||
| 5 | Linear OOA(752, large, F7, 3, 5) | [i] | ||
| 6 | Linear OOA(755, large, F7, 3, 5) | [i] | ||
| 7 | Linear OOA(758, large, F7, 3, 5) | [i] | ||
| 8 | Linear OOA(761, large, F7, 3, 5) | [i] | ||
| 9 | Linear OOA(767, large, F7, 3, 5) | [i] | ||
| 10 | Linear OOA(770, large, F7, 3, 5) | [i] | ||
| 11 | Linear OOA(776, large, F7, 3, 5) | [i] | ||
| 12 | Linear OOA(779, large, F7, 3, 5) | [i] | ||
| 13 | Linear OOA(782, large, F7, 3, 5) | [i] | ||
| 14 | Linear OOA(785, large, F7, 3, 5) | [i] | ||
| 15 | Linear OOA(788, large, F7, 3, 5) | [i] | ||
| 16 | Linear OOA(794, large, F7, 3, 5) | [i] | ||
| 17 | Linear OOA(797, large, F7, 3, 5) | [i] | ||
| 18 | Linear OOA(7100, large, F7, 3, 5) | [i] | ||
| 19 | Linear OOA(7103, large, F7, 3, 5) | [i] | ||
| 20 | Linear OOA(7106, large, F7, 3, 5) | [i] | ||
| 21 | Linear OOA(7109, large, F7, 3, 5) | [i] | ||
| 22 | Linear OOA(745, large, F7, 3, 5) | [i] | OOA Duplication | |