Information on Result #1301858
Linear OA(5133, 15668, F5, 26) (dual of [15668, 15535, 27]-code), using construction X with Varšamov bound based on
- linear OA(5132, 15666, F5, 26) (dual of [15666, 15534, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(25) ⊂ Ce(18) [i] based on
- linear OA(5132, 15667, F5, 25) (dual of [15667, 15535, 26]-code), using Gilbert–Varšamov bound and bm = 5132 > Vbs−1(k−1) = 21 293180 311685 712803 064454 048192 302319 867589 369071 916419 952181 467936 866176 086350 305725 716825 [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(5133, 15668, F5, 2, 26) (dual of [(15668, 2), 31203, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5133, 15668, F5, 3, 26) (dual of [(15668, 3), 46871, 27]-NRT-code) | [i] | ||
| 3 | Digital (107, 133, 15668)-net over F5 | [i] | ||
| 4 | Linear OOA(5133, 7834, F5, 2, 26) (dual of [(7834, 2), 15535, 27]-NRT-code) | [i] | OOA Folding | |