Information on Result #2278870
Linear OA(730, 2406, F7, 9) (dual of [2406, 2376, 10]-code), using 1 times code embedding in larger space based on linear OA(729, 2405, F7, 9) (dual of [2405, 2376, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(729, 2401, F7, 9) (dual of [2401, 2372, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(725, 2401, F7, 8) (dual of [2401, 2376, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(70, 4, F7, 0) (dual of [4, 4, 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
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(730, 1782, F7, 2, 9) (dual of [(1782, 2), 3534, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(730, 1782, F7, 3, 9) (dual of [(1782, 3), 5316, 10]-NRT-code) | [i] | ||
| 3 | Digital (21, 30, 1782)-net over F7 | [i] | ||
| 4 | Linear OOA(730, 1203, F7, 2, 9) (dual of [(1203, 2), 2376, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(730, 802, F7, 3, 9) (dual of [(802, 3), 2376, 10]-NRT-code) | [i] | ||