Information on Result #679325
Linear OA(4157, 16394, F4, 30) (dual of [16394, 16237, 31]-code), using construction XX applied to Ce(29) ⊂ Ce(28) ⊂ Ce(26) 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(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 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
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(4157, 8493, F4, 2, 30) (dual of [(8493, 2), 16829, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4157, 8493, F4, 3, 30) (dual of [(8493, 3), 25322, 31]-NRT-code) | [i] | ||
| 3 | Digital (127, 157, 8493)-net over F4 | [i] | ||
| 4 | Linear OOA(4157, 8197, F4, 2, 30) (dual of [(8197, 2), 16237, 31]-NRT-code) | [i] | OOA Folding | |