Information on Result #1301448
Linear OA(568, 15657, F5, 13) (dual of [15657, 15589, 14]-code), using construction X with Varšamov bound based on
- linear OA(567, 15655, F5, 13) (dual of [15655, 15588, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(561, 15625, F5, 13) (dual of [15625, 15564, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(537, 15625, F5, 8) (dual of [15625, 15588, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(567, 15656, F5, 12) (dual of [15656, 15589, 13]-code), using Gilbert–Varšamov bound and bm = 567 > Vbs−1(k−1) = 1449 566665 589636 844143 050698 362021 410524 391085 [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(568, 15657, F5, 2, 13) (dual of [(15657, 2), 31246, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(568, 15657, F5, 3, 13) (dual of [(15657, 3), 46903, 14]-NRT-code) | [i] | ||
| 3 | Digital (55, 68, 15657)-net over F5 | [i] | ||