Information on Result #696725
Linear OA(3226, 32776, F32, 9) (dual of [32776, 32750, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,3]) based on
- linear OA(3225, 32769, F32, 9) (dual of [32769, 32744, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(3219, 32769, F32, 7) (dual of [32769, 32750, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(3226, 25885, F32, 2, 9) (dual of [(25885, 2), 51744, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (17, 26, 25885)-net over F32 | [i] | ||
| 3 | Linear OOA(3226, 16388, F32, 2, 9) (dual of [(16388, 2), 32750, 10]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3226, 8193, F32, 9, 9) (dual of [(8193, 9), 73711, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |