Information on Result #676056
Linear OA(363, 2214, F3, 12) (dual of [2214, 2151, 13]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
- linear OA(357, 2187, F3, 13) (dual of [2187, 2130, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(336, 2187, F3, 8) (dual of [2187, 2151, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(36, 27, F3, 3) (dual of [27, 21, 4]-code or 27-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(363, 2047, F3, 2, 12) (dual of [(2047, 2), 4031, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(363, 2047, F3, 3, 12) (dual of [(2047, 3), 6078, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(363, 2047, F3, 4, 12) (dual of [(2047, 4), 8125, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(363, 2047, F3, 5, 12) (dual of [(2047, 5), 10172, 13]-NRT-code) | [i] | ||
| 5 | Digital (51, 63, 2047)-net over F3 | [i] | ||
| 6 | Linear OOA(363, 1107, F3, 2, 12) (dual of [(1107, 2), 2151, 13]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(363, 738, F3, 3, 12) (dual of [(738, 3), 2151, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(363, 553, F3, 4, 12) (dual of [(553, 4), 2149, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(363, 442, F3, 5, 12) (dual of [(442, 5), 2147, 13]-NRT-code) | [i] | ||