Information on Result #682323
Linear OA(5134, 390662, F5, 20) (dual of [390662, 390528, 21]-code), using construction X applied to Ce(20) ⊂ Ce(15) based on
- linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(55, 37, F5, 3) (dual of [37, 32, 4]-code or 37-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(5134, 275843, F5, 2, 20) (dual of [(275843, 2), 551552, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5134, 275843, F5, 3, 20) (dual of [(275843, 3), 827395, 21]-NRT-code) | [i] | ||
| 3 | Digital (114, 134, 275843)-net over F5 | [i] | ||
| 4 | Linear OA(5137, 390667, F5, 20) (dual of [390667, 390530, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(5134, 195331, F5, 2, 20) (dual of [(195331, 2), 390528, 21]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(5134, 130220, F5, 3, 20) (dual of [(130220, 3), 390526, 21]-NRT-code) | [i] | ||
| 7 | Linear OOA(5134, 39066, F5, 20, 20) (dual of [(39066, 20), 781186, 21]-NRT-code) | [i] | OA Folding and Stacking | |