Information on Result #1311510
Linear OA(751, 4813, F7, 13) (dual of [4813, 4762, 14]-code), using 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) based on linear OA(750, 4806, F7, 13) (dual of [4806, 4756, 14]-code), using
- trace code [i] based on linear OA(4925, 2403, F49, 13) (dual of [2403, 2378, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(4925, 2401, F49, 13) (dual of [2401, 2376, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 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(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
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
Mode: 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(751, 4813, F7, 2, 13) (dual of [(4813, 2), 9575, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(751, 4813, F7, 3, 13) (dual of [(4813, 3), 14388, 14]-NRT-code) | [i] | ||
| 3 | Digital (38, 51, 4813)-net over F7 | [i] | ||
| 4 | Linear OOA(751, 2406, F7, 2, 13) (dual of [(2406, 2), 4761, 14]-NRT-code) | [i] | OOA Folding | |