Information on Result #682498
Linear OA(5118, 78158, F5, 20) (dual of [78158, 78040, 21]-code), using construction X applied to Ce(20) ⊂ Ce(15) based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(55, 33, F5, 3) (dual of [33, 28, 4]-code or 33-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
Mode: Constructive and 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(5118, 65962, F5, 2, 20) (dual of [(65962, 2), 131806, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5118, 65962, F5, 3, 20) (dual of [(65962, 3), 197768, 21]-NRT-code) | [i] | ||
| 3 | Digital (98, 118, 65962)-net over F5 | [i] | ||
| 4 | Linear OA(5121, 78163, F5, 20) (dual of [78163, 78042, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(5118, 39079, F5, 2, 20) (dual of [(39079, 2), 78040, 21]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5118, 26052, F5, 3, 20) (dual of [(26052, 3), 78038, 21]-NRT-code) | [i] | ||