Information on Result #700254
Linear OA(25644, 65548, F256, 21) (dual of [65548, 65504, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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 | Linear OA(1688, 131096, F16, 21) (dual of [131096, 131008, 22]-code) | [i] | Trace Code | |
| 2 | OA(3271, 65548, S32, 21) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6459, 65548, S64, 21) | [i] | ||
| 4 | OA(12851, 65548, S128, 21) | [i] | ||
| 5 | Linear OA(25654, 65805, F256, 21) (dual of [65805, 65751, 22]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25655, 65808, F256, 21) (dual of [65808, 65753, 22]-code) | [i] | ||
| 7 | Linear OOA(25644, 32774, F256, 2, 21) (dual of [(32774, 2), 65504, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(25644, 21849, F256, 3, 21) (dual of [(21849, 3), 65503, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(25644, 16387, F256, 4, 21) (dual of [(16387, 4), 65504, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(25644, 13109, F256, 5, 21) (dual of [(13109, 5), 65501, 22]-NRT-code) | [i] | ||