Information on Result #678263
Linear OA(4227, 1048652, F4, 28) (dual of [1048652, 1048425, 29]-code), using construction X applied to Ce(28) ⊂ Ce(20) based on
- linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(416, 76, F4, 6) (dual of [76, 60, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 85, F4, 6) (dual of [85, 69, 7]-code), 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 OA(4230, 1048655, F4, 28) (dual of [1048655, 1048425, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4227, 601794, F4, 2, 28) (dual of [(601794, 2), 1203361, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4227, 601794, F4, 3, 28) (dual of [(601794, 3), 1805155, 29]-NRT-code) | [i] | ||
| 4 | Digital (199, 227, 601794)-net over F4 | [i] | ||
| 5 | Linear OA(4230, 1048656, F4, 28) (dual of [1048656, 1048426, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4227, 524326, F4, 2, 28) (dual of [(524326, 2), 1048425, 29]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4227, 349550, F4, 3, 28) (dual of [(349550, 3), 1048423, 29]-NRT-code) | [i] | ||