Information on Result #1021973
Linear OOA(789, large, F7, 3, 8), using generalized (u, u+v)-construction based on
- linear OOA(79, 2796201, F7, 3, 2) (dual of [(2796201, 3), 8388594, 3]-NRT-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OOA(79, 6725601, F7, 3, 2) (dual of [(6725601, 3), 20176794, 3]-NRT-code), using
- linear OOA(725, 2796201, F7, 3, 4) (dual of [(2796201, 3), 8388578, 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(755, 2796201, F7, 3, 8) (dual of [(2796201, 3), 8388548, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(755, large, F7, 8) (dual of [large, large−55, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 20176803 | 79−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 3-folding [i] based on linear OA(755, large, F7, 8) (dual of [large, large−55, 9]-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(789, large, F7, 3, 7) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(789, large, F7, 3, 6) | [i] | ||
| 3 | Linear OOA(789, large, F7, 3, 5) | [i] | ||
| 4 | Linear OOA(789, large, F7, 3, 4) | [i] | ||
| 5 | Linear OOA(789, large, F7, 3, 3) | [i] | ||
| 6 | Linear OOA(795, large, F7, 3, 8) | [i] | NRT-Code Embedding in Larger Space | |
| 7 | Linear OOA(798, large, F7, 3, 8) | [i] | ||
| 8 | Linear OOA(7101, large, F7, 3, 8) | [i] | ||
| 9 | Linear OOA(7110, large, F7, 3, 8) | [i] | ||
| 10 | Linear OOA(790, large, F7, 3, 8) | [i] | OOA Duplication | |