Information on Result #679078
Linear OA(4170, 16399, F4, 32) (dual of [16399, 16229, 33]-code), using construction X applied to Ce(32) ⊂ Ce(29) based on
- linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- 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(41, 15, F4, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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(4170, 9868, F4, 2, 32) (dual of [(9868, 2), 19566, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4170, 9868, F4, 3, 32) (dual of [(9868, 3), 29434, 33]-NRT-code) | [i] | ||
| 3 | Digital (138, 170, 9868)-net over F4 | [i] | ||
| 4 | Linear OOA(4170, 8199, F4, 2, 32) (dual of [(8199, 2), 16228, 33]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4170, 5466, F4, 3, 32) (dual of [(5466, 3), 16228, 33]-NRT-code) | [i] | ||