Information on Result #1311690
Linear OA(763, 410, F7, 23) (dual of [410, 347, 24]-code), using 59 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 9 times 0, 1, 17 times 0, 1, 27 times 0) based on linear OA(758, 346, F7, 23) (dual of [346, 288, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(758, 343, F7, 23) (dual of [343, 285, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(755, 343, F7, 22) (dual of [343, 288, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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(763, 410, F7, 2, 23) (dual of [(410, 2), 757, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(763, 410, F7, 3, 23) (dual of [(410, 3), 1167, 24]-NRT-code) | [i] | ||
| 3 | Digital (40, 63, 410)-net over F7 | [i] | ||
| 4 | Linear OOA(763, 205, F7, 2, 23) (dual of [(205, 2), 347, 24]-NRT-code) | [i] | OOA Folding | |