Information on Result #1567402
Linear OOA(25640, 31770, F256, 3, 18) (dual of [(31770, 3), 95270, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(25640, 31770, F256, 2, 18) (dual of [(31770, 2), 63500, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25640, 32776, F256, 2, 18) (dual of [(32776, 2), 65512, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25640, 65552, F256, 18) (dual of [65552, 65512, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, 65553, F256, 18) (dual of [65553, 65513, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(25640, 65553, F256, 18) (dual of [65553, 65513, 19]-code), using
- OOA 2-folding [i] based on linear OA(25640, 65552, F256, 18) (dual of [65552, 65512, 19]-code), using
Mode: 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 | OOA(12846, 31770, S128, 3, 18) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(25640, 15885, F256, 5, 18) (dual of [(15885, 5), 79385, 19]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(25640, 15885, F256, 6, 18) (dual of [(15885, 6), 95270, 19]-NRT-code) | [i] | ||