Information on Result #682195
Linear OA(5150, 1953166, F5, 20) (dual of [1953166, 1953016, 21]-code), using construction X applied to Ce(20) ⊂ Ce(15) based on
- linear OA(5145, 1953125, F5, 21) (dual of [1953125, 1952980, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(55, 41, F5, 3) (dual of [41, 36, 4]-code or 41-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(5150, 1153410, F5, 2, 20) (dual of [(1153410, 2), 2306670, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5150, 1153410, F5, 3, 20) (dual of [(1153410, 3), 3460080, 21]-NRT-code) | [i] | ||
| 3 | Digital (130, 150, 1153410)-net over F5 | [i] | ||
| 4 | Linear OOA(5150, 976583, F5, 2, 20) (dual of [(976583, 2), 1953016, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5150, 651055, F5, 3, 20) (dual of [(651055, 3), 1953015, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(5150, 195316, F5, 20, 20) (dual of [(195316, 20), 3906170, 21]-NRT-code) | [i] | OA Folding and Stacking | |