Information on Result #823147
Linear OOA(4122, 2097157, F4, 2, 15) (dual of [(2097157, 2), 4194192, 16]-NRT-code), using OOA 2-folding based on linear OA(4122, 4194314, F4, 15) (dual of [4194314, 4194192, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4122, 4194315, F4, 15) (dual of [4194315, 4194193, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(40, 11, F4, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(13) [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(4122, 1848579, F4, 3, 15) (dual of [(1848579, 3), 5545615, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (107, 122, 1848579)-net over F4 | [i] | ||