Information on Result #2272780
Linear OA(4241, 1048656, F4, 30) (dual of [1048656, 1048415, 31]-code), using 2 times code embedding in larger space based on linear OA(4239, 1048654, F4, 30) (dual of [1048654, 1048415, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- linear OA(4221, 1048576, F4, 30) (dual of [1048576, 1048355, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(418, 78, F4, 7) (dual of [78, 60, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(418, 85, F4, 7) (dual of [85, 67, 8]-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 OOA(4241, 544980, F4, 2, 30) (dual of [(544980, 2), 1089719, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4241, 544980, F4, 3, 30) (dual of [(544980, 3), 1634699, 31]-NRT-code) | [i] | ||
| 3 | Digital (211, 241, 544980)-net over F4 | [i] | ||
| 4 | Linear OOA(4241, 349552, F4, 3, 30) (dual of [(349552, 3), 1048415, 31]-NRT-code) | [i] | OOA Folding | |