Information on Result #679312
Linear OA(4189, 16412, F4, 35) (dual of [16412, 16223, 36]-code), using construction XX applied to Ce(34) ⊂ Ce(30) ⊂ Ce(29) based on
- 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(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(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(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-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
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(4189, 11781, F4, 2, 35) (dual of [(11781, 2), 23373, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4189, 11781, F4, 3, 35) (dual of [(11781, 3), 35154, 36]-NRT-code) | [i] | ||
| 3 | Digital (154, 189, 11781)-net over F4 | [i] | ||
| 4 | Linear OOA(4189, 8206, F4, 2, 35) (dual of [(8206, 2), 16223, 36]-NRT-code) | [i] | OOA Folding | |