Information on Result #700270
Linear OA(25630, 65554, F256, 13) (dual of [65554, 65524, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,3]) 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(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(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), 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(12835, 65554, S128, 13) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25630, 42996, F256, 2, 13) (dual of [(42996, 2), 85962, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25630, 42996, F256, 3, 13) (dual of [(42996, 3), 128958, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(25630, 42996, F256, 4, 13) (dual of [(42996, 4), 171954, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(25630, 42996, F256, 5, 13) (dual of [(42996, 5), 214950, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(25630, 42996, F256, 6, 13) (dual of [(42996, 6), 257946, 14]-NRT-code) | [i] | ||
| 7 | Digital (17, 30, 42996)-net over F256 | [i] | ||
| 8 | Linear OOA(25630, 32777, F256, 2, 13) (dual of [(32777, 2), 65524, 14]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25630, 21851, F256, 3, 13) (dual of [(21851, 3), 65523, 14]-NRT-code) | [i] | ||
| 10 | Linear OOA(25630, 16388, F256, 4, 13) (dual of [(16388, 4), 65522, 14]-NRT-code) | [i] | ||
| 11 | Linear OOA(25630, 10925, F256, 13, 13) (dual of [(10925, 13), 141995, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |