Information on Result #2272413
Linear OA(4163, 65578, F4, 26) (dual of [65578, 65415, 27]-code), using 3 times code embedding in larger space based on linear OA(4160, 65575, F4, 26) (dual of [65575, 65415, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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(4163, 37838, F4, 2, 26) (dual of [(37838, 2), 75513, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4163, 37838, F4, 3, 26) (dual of [(37838, 3), 113351, 27]-NRT-code) | [i] | ||
| 3 | Digital (137, 163, 37838)-net over F4 | [i] | ||