Information on Result #696723
Linear OA(3238, 32776, F32, 13) (dual of [32776, 32738, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,5]) based on
- linear OA(3237, 32769, F32, 13) (dual of [32769, 32732, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(3231, 32769, F32, 11) (dual of [32769, 32738, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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 | OA(1648, 32776, S16, 13) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(3245, 32820, F32, 13) (dual of [32820, 32775, 14]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(3238, 18294, F32, 2, 13) (dual of [(18294, 2), 36550, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (25, 38, 18294)-net over F32 | [i] | ||
| 5 | Linear OOA(3238, 16388, F32, 2, 13) (dual of [(16388, 2), 32738, 14]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(3238, 5462, F32, 13, 13) (dual of [(5462, 13), 70968, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |