Information on Result #678137
Linear OA(432, 1048587, F4, 5) (dual of [1048587, 1048555, 6]-code), using construction X applied to Ce(4) ⊂ Ce(2) based on
- linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(421, 1048576, F4, 3) (dual of [1048576, 1048555, 4]-code or 1048576-cap in PG(20,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(432, 1008204, F4, 2, 5) (dual of [(1008204, 2), 2016376, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(432, 1008204, F4, 3, 5) (dual of [(1008204, 3), 3024580, 6]-NRT-code) | [i] | ||
| 3 | Digital (27, 32, 1008204)-net over F4 | [i] | ||
| 4 | Linear OOA(432, 524293, F4, 3, 5) (dual of [(524293, 3), 1572847, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 5 | Linear OOA(432, 524293, F4, 5, 5) (dual of [(524293, 5), 2621433, 6]-NRT-code) | [i] | ||