Information on Result #700248
Linear OA(25668, 65548, F256, 33) (dual of [65548, 65480, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,14]) based on
- linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(25657, 65537, F256, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), 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(32109, 65548, S32, 33) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6491, 65548, S64, 33) | [i] | ||
| 3 | OA(12878, 65548, S128, 33) | [i] | ||
| 4 | Linear OOA(25668, 32774, F256, 2, 33) (dual of [(32774, 2), 65480, 34]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(25668, 21849, F256, 3, 33) (dual of [(21849, 3), 65479, 34]-NRT-code) | [i] | ||
| 6 | Linear OOA(25668, 16387, F256, 4, 33) (dual of [(16387, 4), 65480, 34]-NRT-code) | [i] | ||
| 7 | Linear OOA(25668, 13109, F256, 5, 33) (dual of [(13109, 5), 65477, 34]-NRT-code) | [i] | ||