Information on Result #1311604
Linear OA(772, 4899, F7, 18) (dual of [4899, 4827, 19]-code), using 91 step Varšamov–Edel lengthening with (ri) = (1, 12 times 0, 1, 77 times 0) based on linear OA(770, 4806, F7, 18) (dual of [4806, 4736, 19]-code), using
- trace code [i] based on linear OA(4935, 2403, F49, 18) (dual of [2403, 2368, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(4935, 2401, F49, 18) (dual of [2401, 2366, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [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(772, 4899, F7, 2, 18) (dual of [(4899, 2), 9726, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(772, 4899, F7, 3, 18) (dual of [(4899, 3), 14625, 19]-NRT-code) | [i] | ||
| 3 | Digital (54, 72, 4899)-net over F7 | [i] | ||
| 4 | Linear OOA(772, 2449, F7, 2, 18) (dual of [(2449, 2), 4826, 19]-NRT-code) | [i] | OOA Folding | |