Information on Result #1311663
Linear OA(783, 4849, F7, 21) (dual of [4849, 4766, 22]-code), using 42 step Varšamov–Edel lengthening with (ri) = (1, 41 times 0) based on linear OA(782, 4806, F7, 21) (dual of [4806, 4724, 22]-code), using
- trace code [i] based on linear OA(4941, 2403, F49, 21) (dual of [2403, 2362, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(4941, 2401, F49, 21) (dual of [2401, 2360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4939, 2401, F49, 20) (dual of [2401, 2362, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(20) ⊂ Ce(19) [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(783, 4849, F7, 2, 21) (dual of [(4849, 2), 9615, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(783, 4849, F7, 3, 21) (dual of [(4849, 3), 14464, 22]-NRT-code) | [i] | ||
| 3 | Digital (62, 83, 4849)-net over F7 | [i] | ||
| 4 | Linear OOA(783, 2424, F7, 2, 21) (dual of [(2424, 2), 4765, 22]-NRT-code) | [i] | OOA Folding | |