Information on Result #1833637
OOA(12848, 33028, S128, 2, 17), using discarding parts of the base based on linear OOA(25642, 33028, F256, 2, 17) (dual of [(33028, 2), 66014, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2568, 257, F256, 2, 8) (dual of [(257, 2), 506, 9]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;506,256) [i]
- linear OOA(25634, 32771, F256, 2, 17) (dual of [(32771, 2), 65508, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25634, 65542, F256, 17) (dual of [65542, 65508, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- 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(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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([0,8]) ⊂ C([0,7]) [i] based on
- OOA 2-folding [i] based on linear OA(25634, 65542, F256, 17) (dual of [65542, 65508, 18]-code), using
- linear OOA(2568, 257, F256, 2, 8) (dual of [(257, 2), 506, 9]-NRT-code), using
Mode: Constructive.
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(12848, 16514, S128, 4, 17) | [i] | OOA Folding | |