Information on Result #675521
Linear OA(3199, 6591, F3, 36) (dual of [6591, 6392, 37]-code), using construction X applied to Ce(36) ⊂ Ce(31) based on
- linear OA(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-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(3199, 4032, F3, 2, 36) (dual of [(4032, 2), 7865, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3199, 4032, F3, 3, 36) (dual of [(4032, 3), 11897, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(3199, 4032, F3, 4, 36) (dual of [(4032, 4), 15929, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3199, 4032, F3, 5, 36) (dual of [(4032, 5), 19961, 37]-NRT-code) | [i] | ||
| 5 | Digital (163, 199, 4032)-net over F3 | [i] | ||
| 6 | Linear OOA(3199, 3295, F3, 2, 36) (dual of [(3295, 2), 6391, 37]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3199, 2197, F3, 3, 36) (dual of [(2197, 3), 6392, 37]-NRT-code) | [i] | ||
| 8 | Linear OOA(3199, 1647, F3, 4, 36) (dual of [(1647, 4), 6389, 37]-NRT-code) | [i] | ||
| 9 | Linear OOA(3199, 1318, F3, 5, 36) (dual of [(1318, 5), 6391, 37]-NRT-code) | [i] | ||