Information on Result #1567246
Linear OOA(25618, 31019, F256, 3, 9) (dual of [(31019, 3), 93039, 10]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(25618, 31019, F256, 2, 9) (dual of [(31019, 2), 62020, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25618, 32771, F256, 2, 9) (dual of [(32771, 2), 65524, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25618, 65542, F256, 9) (dual of [65542, 65524, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- 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(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(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- OOA 2-folding [i] based on linear OA(25618, 65542, F256, 9) (dual of [65542, 65524, 10]-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(12821, 31019, S128, 3, 9) | [i] | Discarding Parts of the Base for OOAs | |