Information on Result #700258
Linear OA(25628, 65548, F256, 13) (dual of [65548, 65520, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,4]) based on
- 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(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (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(1656, 131096, F16, 13) (dual of [131096, 131040, 14]-code) | [i] | Trace Code | |
| 2 | OA(12832, 65548, S128, 13) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(25628, 32774, F256, 2, 13) (dual of [(32774, 2), 65520, 14]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(25628, 21849, F256, 3, 13) (dual of [(21849, 3), 65519, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(25628, 16387, F256, 4, 13) (dual of [(16387, 4), 65520, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(25628, 13109, F256, 5, 13) (dual of [(13109, 5), 65517, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(25628, 10924, F256, 13, 13) (dual of [(10924, 13), 141984, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |