Information on Result #1013650
Linear OOA(731, 5767605, F7, 3, 4) (dual of [(5767605, 3), 17302784, 5]-NRT-code), using (u, u+v)-construction based on
- linear OOA(75, 2801, F7, 3, 2) (dual of [(2801, 3), 8398, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(75, 2801, F7, 2, 2) (dual of [(2801, 2), 5597, 3]-NRT-code), using
- appending kth column [i] based on linear OA(75, 2801, F7, 2) (dual of [2801, 2796, 3]-code), using
- Hamming code H(5,7) [i]
- appending kth column [i] based on linear OA(75, 2801, F7, 2) (dual of [2801, 2796, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(75, 2801, F7, 2, 2) (dual of [(2801, 2), 5597, 3]-NRT-code), using
- linear OOA(726, 5764804, F7, 3, 4) (dual of [(5764804, 3), 17294386, 5]-NRT-code), using
- trace code [i] based on linear OOA(4913, 2882402, F49, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- 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(499, 5764801, F49, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- trace code [i] based on linear OOA(4913, 2882402, F49, 3, 4) (dual of [(2882402, 3), 8647193, 5]-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(731, 5767605, F7, 4, 4) (dual of [(5767605, 4), 23070389, 5]-NRT-code) | [i] | Appending kth Column | |