Information on Result #1301721
Linear OA(5109, 15668, F5, 21) (dual of [15668, 15559, 22]-code), using construction X with Varšamov bound based on
- linear OA(5108, 15666, F5, 21) (dual of [15666, 15558, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(511, 41, F5, 6) (dual of [41, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(511, 45, F5, 6) (dual of [45, 34, 7]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(5108, 15667, F5, 20) (dual of [15667, 15559, 21]-code), using Gilbert–Varšamov bound and bm = 5108 > Vbs−1(k−1) = 113 145956 560424 515557 002505 605868 992358 850643 891009 891679 054137 181742 766425 [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(5109, 15668, F5, 2, 21) (dual of [(15668, 2), 31227, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5109, 15668, F5, 3, 21) (dual of [(15668, 3), 46895, 22]-NRT-code) | [i] | ||
| 3 | Digital (88, 109, 15668)-net over F5 | [i] | ||
| 4 | Linear OOA(5109, 7834, F5, 2, 21) (dual of [(7834, 2), 15559, 22]-NRT-code) | [i] | OOA Folding | |