Information on Result #954244
Linear OOA(3214, 19701, F3, 3, 31) (dual of [(19701, 3), 58889, 32]-NRT-code), using OOA 3-folding based on linear OA(3214, 59103, F3, 31) (dual of [59103, 58889, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3212, 59101, F3, 31) (dual of [59101, 58889, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(311, 51, F3, 5) (dual of [51, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
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(3214, 19701, F3, 3, 30) (dual of [(19701, 3), 58889, 31]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3215, 19701, F3, 3, 31) (dual of [(19701, 3), 58888, 32]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3216, 19701, F3, 3, 31) (dual of [(19701, 3), 58887, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3213, 19700, F3, 3, 30) (dual of [(19700, 3), 58887, 31]-NRT-code) | [i] | Truncation for OOAs | |