Information on Result #952844
Linear OOA(3141, 59062, F3, 3, 19) (dual of [(59062, 3), 177045, 20]-NRT-code), using OOA 3-folding based on linear OA(3141, 177186, F3, 19) (dual of [177186, 177045, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3141, 177188, F3, 19) (dual of [177188, 177047, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
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(3141, 59062, F3, 4, 19) (dual of [(59062, 4), 236107, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3141, 59062, F3, 5, 19) (dual of [(59062, 5), 295169, 20]-NRT-code) | [i] | ||
| 3 | Digital (122, 141, 59062)-net over F3 | [i] | ||