Information on Result #952852
Linear OOA(3153, 177160, F3, 3, 19) (dual of [(177160, 3), 531327, 20]-NRT-code), using OOA 3-folding based on linear OA(3153, 531480, F3, 19) (dual of [531480, 531327, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3153, 531482, F3, 19) (dual of [531482, 531329, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, 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(3153, 177160, F3, 4, 19) (dual of [(177160, 4), 708487, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3153, 177160, F3, 5, 19) (dual of [(177160, 5), 885647, 20]-NRT-code) | [i] | ||
| 3 | Digital (134, 153, 177160)-net over F3 | [i] | ||