Information on Result #896299
Linear OOA(761, 6088122, F7, 2, 7) (dual of [(6088122, 2), 12176183, 8]-NRT-code), using (u, u+v)-construction based on
- linear OOA(711, 323318, F7, 2, 3) (dual of [(323318, 2), 646625, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(711, 323318, F7, 3) (dual of [323318, 323307, 4]-code or 323318-cap in PG(10,7)), 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
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, 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(761, 3044061, F7, 3, 7) (dual of [(3044061, 3), 9132122, 8]-NRT-code) | [i] | OOA Folding | |