Information on Result #1301450
Linear OA(569, 15659, F5, 13) (dual of [15659, 15590, 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, 15657, F5, 12) (dual of [15657, 15590, 13]-code), using Gilbert–Varšamov bound and bm = 567 > Vbs−1(k−1) = 1450 585839 659587 708339 692858 731465 423762 358625 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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(569, 15659, F5, 2, 13) (dual of [(15659, 2), 31249, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(569, 15659, F5, 3, 13) (dual of [(15659, 3), 46908, 14]-NRT-code) | [i] | ||
| 3 | Digital (56, 69, 15659)-net over F5 | [i] | ||