Information on Result #2506269
Linear OOA(781, large, F7, 2, 7), using 9 times NRT-code embedding in larger space based on linear OOA(763, large, F7, 2, 7), using
- (u, u+v)-construction [i] based on
- linear OOA(713, 6120101, F7, 2, 3) (dual of [(6120101, 2), 12240189, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(713, 6120101, F7, 3) (dual of [6120101, 6120088, 4]-code or 6120101-cap in PG(12,7)), using
- linear OOA(750, 5764804, F7, 2, 7) (dual of [(5764804, 2), 11529558, 8]-NRT-code), using
- trace code [i] based on linear OOA(4925, 2882402, F49, 2, 7) (dual of [(2882402, 2), 5764779, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4925, 5764804, F49, 7) (dual of [5764804, 5764779, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- OOA 2-folding [i] based on linear OA(4925, 5764804, F49, 7) (dual of [5764804, 5764779, 8]-code), using
- trace code [i] based on linear OOA(4925, 2882402, F49, 2, 7) (dual of [(2882402, 2), 5764779, 8]-NRT-code), using
- linear OOA(713, 6120101, F7, 2, 3) (dual of [(6120101, 2), 12240189, 4]-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(782, large, F7, 2, 7) | [i] | OOA Duplication | |