Information on Result #679281
Linear OA(4245, 16412, F4, 46) (dual of [16412, 16167, 47]-code), using construction XX applied to Ce(45) ⊂ Ce(41) ⊂ Ce(40) based on
- linear OA(4239, 16384, F4, 46) (dual of [16384, 16145, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4218, 16384, F4, 42) (dual of [16384, 16166, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(4245, 12510, F4, 2, 46) (dual of [(12510, 2), 24775, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4245, 12510, F4, 3, 46) (dual of [(12510, 3), 37285, 47]-NRT-code) | [i] | ||
| 3 | Digital (199, 245, 12510)-net over F4 | [i] | ||
| 4 | Linear OOA(4245, 8206, F4, 2, 46) (dual of [(8206, 2), 16167, 47]-NRT-code) | [i] | OOA Folding | |