Information on Result #1021719
Linear OOA(7105, large, F7, 3, 9), using generalized (u, u+v)-construction based on
- linear OOA(71, 960800, F7, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(71, s, F7, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(71, s, F7, 3, 1) for arbitrarily large s, using
- linear OOA(71, 960800, F7, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code) (see above)
- linear OOA(71, 960800, F7, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code) (see above)
- linear OOA(78, 960800, F7, 3, 2) (dual of [(960800, 3), 2882392, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(78, 960800, F7, 2, 2) (dual of [(960800, 2), 1921592, 3]-NRT-code), using
- appending kth column [i] based on linear OA(78, 960800, F7, 2) (dual of [960800, 960792, 3]-code), using
- Hamming code H(8,7) [i]
- appending kth column [i] based on linear OA(78, 960800, F7, 2) (dual of [960800, 960792, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(78, 960800, F7, 2, 2) (dual of [(960800, 2), 1921592, 3]-NRT-code), using
- linear OOA(712, 1067080, F7, 3, 3) (dual of [(1067080, 3), 3201228, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(712, 1067080, F7, 2, 3) (dual of [(1067080, 2), 2134148, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(712, 1067080, F7, 3) (dual of [1067080, 1067068, 4]-code or 1067080-cap in PG(11,7)), using
- appending kth column [i] based on linear OOA(712, 1067080, F7, 2, 3) (dual of [(1067080, 2), 2134148, 4]-NRT-code), using
- linear OOA(725, 1921603, F7, 3, 4) (dual of [(1921603, 3), 5764784, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(725, 2882404, F7, 3, 4) (dual of [(2882404, 3), 8647187, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(725, 5764808, F7, 4) (dual of [5764808, 5764783, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(725, 5764809, F7, 4) (dual of [5764809, 5764784, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(725, 5764801, F7, 4) (dual of [5764801, 5764776, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(717, 5764801, F7, 3) (dual of [5764801, 5764784, 4]-code or 5764801-cap in PG(16,7)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(70, 8, F7, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(725, 5764809, F7, 4) (dual of [5764809, 5764784, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(725, 5764808, F7, 4) (dual of [5764808, 5764783, 5]-code), using
- discarding factors / shortening the dual code based on linear OOA(725, 2882404, F7, 3, 4) (dual of [(2882404, 3), 8647187, 5]-NRT-code), using
- linear OOA(757, 1921603, F7, 3, 9) (dual of [(1921603, 3), 5764752, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(757, 5764809, F7, 9) (dual of [5764809, 5764752, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(757, 5764801, F7, 9) (dual of [5764801, 5764744, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(749, 5764801, F7, 8) (dual of [5764801, 5764752, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(70, 8, F7, 0) (dual of [8, 8, 1]-code) (see above)
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- OOA 3-folding [i] based on linear OA(757, 5764809, F7, 9) (dual of [5764809, 5764752, 10]-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(7105, large, F7, 3, 8) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(7105, large, F7, 3, 7) | [i] | ||
| 3 | Linear OOA(7105, large, F7, 3, 6) | [i] | ||
| 4 | Linear OOA(7105, large, F7, 3, 5) | [i] | ||
| 5 | Linear OOA(7105, large, F7, 3, 4) | [i] | ||
| 6 | Linear OOA(7105, large, F7, 3, 3) | [i] | ||
| 7 | Linear OOA(7106, large, F7, 3, 9) | [i] | OOA Duplication | |