Information on Result #1437131
Linear OOA(571, 390664, F5, 2, 10) (dual of [(390664, 2), 781257, 11]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(571, 390664, F5, 10) (dual of [390664, 390593, 11]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(570, 390662, F5, 10) (dual of [390662, 390592, 11]-code), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- linear OA(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(55, 37, F5, 3) (dual of [37, 32, 4]-code or 37-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- linear OA(570, 390663, F5, 9) (dual of [390663, 390593, 10]-code), using Gilbert–Varšamov bound and bm = 570 > Vbs−1(k−1) = 881 738605 387522 443526 611262 395026 581465 113865 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(570, 390662, F5, 10) (dual of [390662, 390592, 11]-code), 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(571, 195332, F5, 3, 10) (dual of [(195332, 3), 585925, 11]-NRT-code) | [i] | OOA Folding | |