Information on Result #679125
Linear OA(4167, 16410, F4, 31) (dual of [16410, 16243, 32]-code), using construction X applied to Ce(30) ⊂ Ce(26) 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(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(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-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
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(4167, 10848, F4, 2, 31) (dual of [(10848, 2), 21529, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4167, 10848, F4, 3, 31) (dual of [(10848, 3), 32377, 32]-NRT-code) | [i] | ||
| 3 | Digital (136, 167, 10848)-net over F4 | [i] | ||
| 4 | Linear OOA(4167, 8205, F4, 2, 31) (dual of [(8205, 2), 16243, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4167, 5470, F4, 3, 31) (dual of [(5470, 3), 16243, 32]-NRT-code) | [i] | ||