Information on Result #679722
Linear OA(490, 4119, F4, 19) (dual of [4119, 4029, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
- linear OA(485, 4096, F4, 19) (dual of [4096, 4011, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(467, 4096, F4, 15) (dual of [4096, 4029, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(45, 23, F4, 3) (dual of [23, 18, 4]-code or 23-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(490, 3382, F4, 2, 19) (dual of [(3382, 2), 6674, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(490, 3382, F4, 3, 19) (dual of [(3382, 3), 10056, 20]-NRT-code) | [i] | ||
| 3 | Digital (71, 90, 3382)-net over F4 | [i] | ||
| 4 | Linear OOA(490, 2059, F4, 2, 19) (dual of [(2059, 2), 4028, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(490, 1373, F4, 3, 19) (dual of [(1373, 3), 4029, 20]-NRT-code) | [i] | ||