Information on Result #731030
Linear OA(746, 4806, F7, 12) (dual of [4806, 4760, 13]-code), using trace code based on linear OA(4923, 2403, F49, 12) (dual of [2403, 2380, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4921, 2401, F49, 11) (dual of [2401, 2380, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(747, 4807, F7, 12) (dual of [4807, 4760, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(747, 4813, F7, 12) (dual of [4813, 4766, 13]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(748, 4859, F7, 12) (dual of [4859, 4811, 13]-code) | [i] | ||
| 4 | Linear OA(749, 5096, F7, 12) (dual of [5096, 5047, 13]-code) | [i] | ||
| 5 | Linear OA(747, 4808, F7, 12) (dual of [4808, 4761, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(746, 2403, F7, 2, 12) (dual of [(2403, 2), 4760, 13]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(746, 1602, F7, 3, 12) (dual of [(1602, 3), 4760, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(746, 801, F7, 12, 12) (dual of [(801, 12), 9566, 13]-NRT-code) | [i] | OA Folding and Stacking | |