Information on Result #676024
Linear OA(3163, 2216, F3, 34) (dual of [2216, 2053, 35]-code), using construction X applied to Ce(33) ⊂ Ce(28) based on
- linear OA(3155, 2187, F3, 34) (dual of [2187, 2032, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3134, 2187, F3, 29) (dual of [2187, 2053, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(38, 29, F3, 4) (dual of [29, 21, 5]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), 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(3163, 1635, F3, 2, 34) (dual of [(1635, 2), 3107, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3163, 1635, F3, 3, 34) (dual of [(1635, 3), 4742, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3163, 1635, F3, 4, 34) (dual of [(1635, 4), 6377, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(3163, 1635, F3, 5, 34) (dual of [(1635, 5), 8012, 35]-NRT-code) | [i] | ||
| 5 | Digital (129, 163, 1635)-net over F3 | [i] | ||
| 6 | Linear OOA(3163, 1108, F3, 2, 34) (dual of [(1108, 2), 2053, 35]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3163, 554, F3, 4, 34) (dual of [(554, 4), 2053, 35]-NRT-code) | [i] | ||
| 8 | Linear OOA(3163, 443, F3, 5, 34) (dual of [(443, 5), 2052, 35]-NRT-code) | [i] | ||