Information on Result #678185
Linear OA(444, 1048597, F4, 6) (dual of [1048597, 1048553, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
- linear OA(441, 1048576, F4, 6) (dual of [1048576, 1048535, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
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(444, 1048597, F4, 2, 6) (dual of [(1048597, 2), 2097150, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(444, 1048597, F4, 3, 6) (dual of [(1048597, 3), 3145747, 7]-NRT-code) | [i] | ||
| 3 | Digital (38, 44, 1048597)-net over F4 | [i] | ||
| 4 | Linear OOA(444, 524298, F4, 2, 6) (dual of [(524298, 2), 1048552, 7]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(444, 349532, F4, 3, 6) (dual of [(349532, 3), 1048552, 7]-NRT-code) | [i] | ||
| 6 | Linear OOA(444, 349532, F4, 6, 6) (dual of [(349532, 6), 2097148, 7]-NRT-code) | [i] | OA Folding and Stacking | |