Information on Result #731016
Linear OA(722, 4806, F7, 6) (dual of [4806, 4784, 7]-code), using trace code based on linear OA(4911, 2403, F49, 6) (dual of [2403, 2392, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4911, 2401, F49, 6) (dual of [2401, 2390, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(499, 2401, F49, 5) (dual of [2401, 2392, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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 OA(723, 4807, F7, 6) (dual of [4807, 4784, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(722, 4806, F7, 2, 6) (dual of [(4806, 2), 9590, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(722, 4806, F7, 3, 6) (dual of [(4806, 3), 14396, 7]-NRT-code) | [i] | ||
| 4 | Digital (16, 22, 4806)-net over F7 | [i] | ||
| 5 | Linear OA(723, 4935, F7, 6) (dual of [4935, 4912, 7]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(724, 5592, F7, 6) (dual of [5592, 5568, 7]-code) | [i] | ||
| 7 | Linear OA(723, 4808, F7, 6) (dual of [4808, 4785, 7]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(722, 2403, F7, 2, 6) (dual of [(2403, 2), 4784, 7]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(722, 1602, F7, 3, 6) (dual of [(1602, 3), 4784, 7]-NRT-code) | [i] | ||
| 10 | Linear OOA(722, 1602, F7, 6, 6) (dual of [(1602, 6), 9590, 7]-NRT-code) | [i] | OA Folding and Stacking | |