Information on Result #823622
Linear OOA(4173, 2097173, F4, 2, 20) (dual of [(2097173, 2), 4194173, 21]-NRT-code), using OOA 2-folding based on linear OA(4173, 4194346, F4, 20) (dual of [4194346, 4194173, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4173, 4194347, F4, 20) (dual of [4194347, 4194174, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [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(4173, 2097173, F4, 3, 20) (dual of [(2097173, 3), 6291346, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (153, 173, 2097173)-net over F4 | [i] | ||