Information on Result #675829
Linear OA(3177, 2224, F3, 36) (dual of [2224, 2047, 37]-code), using construction X applied to C([0,18]) ⊂ C([0,15]) based on
- linear OA(3169, 2188, F3, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3141, 2188, F3, 31) (dual of [2188, 2047, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(38, 36, F3, 4) (dual of [36, 28, 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 OA(3181, 2228, F3, 36) (dual of [2228, 2047, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3182, 2229, F3, 36) (dual of [2229, 2047, 37]-code) | [i] | ||
| 3 | Linear OOA(3177, 1965, F3, 2, 36) (dual of [(1965, 2), 3753, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3177, 1965, F3, 3, 36) (dual of [(1965, 3), 5718, 37]-NRT-code) | [i] | ||
| 5 | Linear OOA(3177, 1965, F3, 4, 36) (dual of [(1965, 4), 7683, 37]-NRT-code) | [i] | ||
| 6 | Linear OOA(3177, 1965, F3, 5, 36) (dual of [(1965, 5), 9648, 37]-NRT-code) | [i] | ||
| 7 | Digital (141, 177, 1965)-net over F3 | [i] | ||
| 8 | Linear OA(3179, 2227, F3, 36) (dual of [2227, 2048, 37]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(3180, 2229, F3, 36) (dual of [2229, 2049, 37]-code) | [i] | ||
| 10 | Linear OA(3181, 2231, F3, 36) (dual of [2231, 2050, 37]-code) | [i] | ||
| 11 | Linear OA(3182, 2233, F3, 36) (dual of [2233, 2051, 37]-code) | [i] | ||
| 12 | Linear OOA(3177, 1112, F3, 2, 36) (dual of [(1112, 2), 2047, 37]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(3177, 741, F3, 3, 36) (dual of [(741, 3), 2046, 37]-NRT-code) | [i] | ||
| 14 | Linear OOA(3177, 556, F3, 4, 36) (dual of [(556, 4), 2047, 37]-NRT-code) | [i] | ||
| 15 | Linear OOA(3177, 444, F3, 5, 36) (dual of [(444, 5), 2043, 37]-NRT-code) | [i] | ||