Information on Result #679327
Linear OA(4161, 16412, F4, 30) (dual of [16412, 16251, 31]-code), using construction XX applied to Ce(29) ⊂ Ce(25) ⊂ Ce(24) based on
- linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(4161, 10359, F4, 2, 30) (dual of [(10359, 2), 20557, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4161, 10359, F4, 3, 30) (dual of [(10359, 3), 30916, 31]-NRT-code) | [i] | ||
| 3 | Digital (131, 161, 10359)-net over F4 | [i] | ||
| 4 | Linear OOA(4161, 8206, F4, 2, 30) (dual of [(8206, 2), 16251, 31]-NRT-code) | [i] | OOA Folding | |