Information on Result #679117
Linear OA(4209, 16410, F4, 39) (dual of [16410, 16201, 40]-code), using construction X applied to Ce(38) ⊂ Ce(34) based on
- linear OA(4204, 16384, F4, 39) (dual of [16384, 16180, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4183, 16384, F4, 35) (dual of [16384, 16201, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(4209, 11810, F4, 2, 39) (dual of [(11810, 2), 23411, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4209, 11810, F4, 3, 39) (dual of [(11810, 3), 35221, 40]-NRT-code) | [i] | ||
| 3 | Digital (170, 209, 11810)-net over F4 | [i] | ||
| 4 | Linear OOA(4209, 8205, F4, 2, 39) (dual of [(8205, 2), 16201, 40]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4209, 5470, F4, 3, 39) (dual of [(5470, 3), 16201, 40]-NRT-code) | [i] | ||