Information on Result #823069
Linear OOA(4118, 2097173, F4, 2, 14) (dual of [(2097173, 2), 4194228, 15]-NRT-code), using OOA 2-folding based on linear OA(4118, 4194346, F4, 14) (dual of [4194346, 4194228, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4118, 4194347, F4, 14) (dual of [4194347, 4194229, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(467, 4194304, F4, 9) (dual of [4194304, 4194237, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
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(2236, 4194346, F2, 2, 14) (dual of [(4194346, 2), 8388456, 15]-NRT-code) | [i] | Trace Code for OOAs | |
| 2 | Linear OOA(4118, 2097173, F4, 3, 14) (dual of [(2097173, 3), 6291401, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (104, 118, 2097173)-net over F4 | [i] | ||