Information on Result #738454
Linear OA(741, 16830, F7, 9) (dual of [16830, 16789, 10]-code), using (u, u+v)-construction based on
- linear OA(75, 18, F7, 4) (dual of [18, 13, 5]-code), using
- linear OA(736, 16812, F7, 9) (dual of [16812, 16776, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(70, 5, F7, 0) (dual of [5, 5, 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(8) ⊂ Ce(7) [i] based on
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(741, 16830, F7, 2, 9) (dual of [(16830, 2), 33619, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(741, 16830, F7, 3, 9) (dual of [(16830, 3), 50449, 10]-NRT-code) | [i] | ||
| 3 | Digital (32, 41, 16830)-net over F7 | [i] | ||
| 4 | Linear OOA(741, 8415, F7, 2, 9) (dual of [(8415, 2), 16789, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(741, 5610, F7, 3, 9) (dual of [(5610, 3), 16789, 10]-NRT-code) | [i] | ||