Information on Result #682707
Linear OA(5150, 15654, F5, 30) (dual of [15654, 15504, 31]-code), using construction X applied to Ce(30) ⊂ Ce(25) based on
- linear OA(5145, 15625, F5, 31) (dual of [15625, 15480, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-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, 14787, F5, 2, 30) (dual of [(14787, 2), 29424, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5150, 14787, F5, 3, 30) (dual of [(14787, 3), 44211, 31]-NRT-code) | [i] | ||
| 3 | Digital (120, 150, 14787)-net over F5 | [i] | ||
| 4 | Linear OOA(5150, 7827, F5, 2, 30) (dual of [(7827, 2), 15504, 31]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5150, 5218, F5, 3, 30) (dual of [(5218, 3), 15504, 31]-NRT-code) | [i] | ||