Information on Result #953280
Linear OOA(3187, 177161, F3, 3, 23) (dual of [(177161, 3), 531296, 24]-NRT-code), using OOA 3-folding based on linear OA(3187, 531483, F3, 23) (dual of [531483, 531296, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(3181, 531441, F3, 23) (dual of [531441, 531260, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3190, 177162, F3, 3, 23) (dual of [(177162, 3), 531296, 24]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3188, 177161, F3, 3, 23) (dual of [(177161, 3), 531295, 24]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3189, 177161, F3, 3, 23) (dual of [(177161, 3), 531294, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(3187, 165455, F3, 4, 23) (dual of [(165455, 4), 661633, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3187, 165455, F3, 5, 23) (dual of [(165455, 5), 827088, 24]-NRT-code) | [i] | ||
| 6 | Digital (164, 187, 165455)-net over F3 | [i] | ||