Information on Result #700243
Linear OA(25630, 65542, F256, 15) (dual of [65542, 65512, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 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 OA(1660, 131084, F16, 15) (dual of [131084, 131024, 16]-code) | [i] | Trace Code | |
| 2 | OA(3248, 65542, S32, 15) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6440, 65542, S64, 15) | [i] | ||
| 4 | OA(12835, 65542, S128, 15) | [i] | ||
| 5 | Linear OA(25637, 65799, F256, 15) (dual of [65799, 65762, 16]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25638, 65802, F256, 15) (dual of [65802, 65764, 16]-code) | [i] | ||
| 7 | Linear OOA(25630, 32771, F256, 2, 15) (dual of [(32771, 2), 65512, 16]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(25630, 21847, F256, 3, 15) (dual of [(21847, 3), 65511, 16]-NRT-code) | [i] | ||
| 9 | Linear OOA(25630, 16385, F256, 4, 15) (dual of [(16385, 4), 65510, 16]-NRT-code) | [i] | ||
| 10 | Linear OOA(25630, 13108, F256, 5, 15) (dual of [(13108, 5), 65510, 16]-NRT-code) | [i] | ||
| 11 | Linear OOA(25630, 9363, F256, 15, 15) (dual of [(9363, 15), 140415, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |