Information on Result #731024
Linear OA(734, 4806, F7, 9) (dual of [4806, 4772, 10]-code), using trace code based on linear OA(4917, 2403, F49, 9) (dual of [2403, 2386, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(4917, 2401, F49, 9) (dual of [2401, 2384, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(4915, 2401, F49, 8) (dual of [2401, 2386, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 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
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(734, 4806, F7, 2, 9) (dual of [(4806, 2), 9578, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(734, 4806, F7, 3, 9) (dual of [(4806, 3), 14384, 10]-NRT-code) | [i] | ||
| 3 | Digital (25, 34, 4806)-net over F7 | [i] | ||
| 4 | Linear OOA(734, 2403, F7, 2, 9) (dual of [(2403, 2), 4772, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(734, 1602, F7, 3, 9) (dual of [(1602, 3), 4772, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(734, 1201, F7, 9, 9) (dual of [(1201, 9), 10775, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |