Information on Result #679080
Linear OA(4163, 16399, F4, 31) (dual of [16399, 16236, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(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 OA(4164, 16400, F4, 31) (dual of [16400, 16236, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4163, 8956, F4, 2, 31) (dual of [(8956, 2), 17749, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4163, 8956, F4, 3, 31) (dual of [(8956, 3), 26705, 32]-NRT-code) | [i] | ||
| 4 | Digital (132, 163, 8956)-net over F4 | [i] | ||
| 5 | Linear OOA(4163, 8199, F4, 2, 31) (dual of [(8199, 2), 16235, 32]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4163, 5466, F4, 3, 31) (dual of [(5466, 3), 16235, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(4163, 1093, F4, 31, 31) (dual of [(1093, 31), 33720, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |