Information on Result #879988
Linear OOA(25619, 32772, F256, 2, 9) (dual of [(32772, 2), 65525, 10]-NRT-code), using OOA 2-folding based on linear OA(25619, 65544, F256, 9) (dual of [65544, 65525, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), 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 OOA(25619, 32772, F256, 3, 9) (dual of [(32772, 3), 98297, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25619, 32772, F256, 4, 9) (dual of [(32772, 4), 131069, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(25619, 32772, F256, 5, 9) (dual of [(32772, 5), 163841, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(25619, 32772, F256, 6, 9) (dual of [(32772, 6), 196613, 10]-NRT-code) | [i] | ||
| 5 | Digital (10, 19, 32772)-net over F256 | [i] | ||