Information on Result #700271
Linear OA(25668, 65560, F256, 31) (dual of [65560, 65492, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,11]) based on
- linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), 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, 65560, S32, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(12878, 65560, S128, 31) | [i] | ||
| 3 | Linear OOA(25668, 32780, F256, 2, 31) (dual of [(32780, 2), 65492, 32]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(25668, 21853, F256, 3, 31) (dual of [(21853, 3), 65491, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(25668, 16390, F256, 4, 31) (dual of [(16390, 4), 65492, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(25668, 13112, F256, 5, 31) (dual of [(13112, 5), 65492, 32]-NRT-code) | [i] | ||