Information on Result #1301571
Linear OA(589, 390666, F5, 13) (dual of [390666, 390577, 14]-code), using construction X with Varšamov bound based on
- linear OA(588, 390664, F5, 13) (dual of [390664, 390576, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(581, 390625, F5, 13) (dual of [390625, 390544, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(549, 390625, F5, 8) (dual of [390625, 390576, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(57, 39, F5, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(588, 390665, F5, 12) (dual of [390665, 390577, 13]-code), using Gilbert–Varšamov bound and bm = 588 > Vbs−1(k−1) = 3 398469 823732 163958 679189 960723 656188 181951 483795 999341 157857 [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
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(589, 390666, F5, 2, 13) (dual of [(390666, 2), 781243, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(589, 390666, F5, 3, 13) (dual of [(390666, 3), 1171909, 14]-NRT-code) | [i] | ||
| 3 | Digital (76, 89, 390666)-net over F5 | [i] | ||
| 4 | Linear OOA(589, 195333, F5, 2, 13) (dual of [(195333, 2), 390577, 14]-NRT-code) | [i] | OOA Folding | |