Information on Result #2266438
Linear OA(3196, 6629, F3, 33) (dual of [6629, 6433, 34]-code), using 3 times code embedding in larger space based on linear OA(3193, 6626, F3, 33) (dual of [6626, 6433, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- 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(3129, 6562, F3, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(316, 64, F3, 7) (dual of [64, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-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(3196, 6197, F3, 2, 33) (dual of [(6197, 2), 12198, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3196, 6197, F3, 3, 33) (dual of [(6197, 3), 18395, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3196, 6197, F3, 4, 33) (dual of [(6197, 4), 24592, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3196, 6197, F3, 5, 33) (dual of [(6197, 5), 30789, 34]-NRT-code) | [i] | ||
| 5 | Digital (163, 196, 6197)-net over F3 | [i] | ||