Information on Result #736969
Linear OA(3172, 6605, F3, 31) (dual of [6605, 6433, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,12]) based on
- linear OA(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (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(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-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(3172, 6605, F3, 30) (dual of [6605, 6433, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3174, 6607, F3, 31) (dual of [6607, 6433, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(3175, 6608, F3, 31) (dual of [6608, 6433, 32]-code) | [i] | ||
| 4 | Linear OA(3176, 6609, F3, 31) (dual of [6609, 6433, 32]-code) | [i] | ||
| 5 | Linear OA(3171, 6604, F3, 30) (dual of [6604, 6433, 31]-code) | [i] | Truncation | |
| 6 | Linear OA(3176, 6610, F3, 31) (dual of [6610, 6434, 32]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(3172, 3302, F3, 2, 31) (dual of [(3302, 2), 6432, 32]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3172, 1651, F3, 4, 31) (dual of [(1651, 4), 6432, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(3172, 1321, F3, 5, 31) (dual of [(1321, 5), 6433, 32]-NRT-code) | [i] | ||