Information on Result #813439
Linear OOA(3101, 3291, F3, 2, 18) (dual of [(3291, 2), 6481, 19]-NRT-code), using OOA 2-folding based on linear OA(3101, 6582, F3, 18) (dual of [6582, 6481, 19]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(381, 6562, F3, 15) (dual of [6562, 6481, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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(3101, 3291, F3, 3, 18) (dual of [(3291, 3), 9772, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3101, 3291, F3, 4, 18) (dual of [(3291, 4), 13063, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(3101, 3291, F3, 5, 18) (dual of [(3291, 5), 16354, 19]-NRT-code) | [i] | ||
| 4 | Digital (83, 101, 3291)-net over F3 | [i] | ||