Information on Result #675313
Linear OA(3197, 6582, F3, 36) (dual of [6582, 6385, 37]-code), using construction X applied to C([0,18]) ⊂ C([0,16]) based on
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3177, 6562, F3, 33) (dual of [6562, 6385, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-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(3197, 3778, F3, 2, 36) (dual of [(3778, 2), 7359, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3197, 3778, F3, 3, 36) (dual of [(3778, 3), 11137, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(3197, 3778, F3, 4, 36) (dual of [(3778, 4), 14915, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(3197, 3778, F3, 5, 36) (dual of [(3778, 5), 18693, 37]-NRT-code) | [i] | ||
| 5 | Digital (161, 197, 3778)-net over F3 | [i] | ||
| 6 | Linear OOA(3197, 3291, F3, 2, 36) (dual of [(3291, 2), 6385, 37]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3197, 2194, F3, 3, 36) (dual of [(2194, 3), 6385, 37]-NRT-code) | [i] | ||