Information on Result #700259
Linear OA(25624, 65548, F256, 11) (dual of [65548, 65524, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,3]) based on
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (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(12828, 65548, S128, 11) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25624, 32774, F256, 2, 11) (dual of [(32774, 2), 65524, 12]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(25624, 21849, F256, 3, 11) (dual of [(21849, 3), 65523, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(25624, 16387, F256, 4, 11) (dual of [(16387, 4), 65524, 12]-NRT-code) | [i] | ||
| 5 | Linear OOA(25624, 13109, F256, 5, 11) (dual of [(13109, 5), 65521, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(25624, 13109, F256, 6, 11) (dual of [(13109, 6), 78630, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 7 | Linear OOA(25624, 13109, F256, 11, 11) (dual of [(13109, 11), 144175, 12]-NRT-code) | [i] | ||