Information on Result #880045
Linear OOA(25629, 32775, F256, 2, 13) (dual of [(32775, 2), 65521, 14]-NRT-code), using OOA 2-folding based on linear OA(25629, 65550, F256, 13) (dual of [65550, 65521, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), 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(25629, 32775, F256, 3, 13) (dual of [(32775, 3), 98296, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25629, 32775, F256, 4, 13) (dual of [(32775, 4), 131071, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(25629, 32775, F256, 5, 13) (dual of [(32775, 5), 163846, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(25629, 32775, F256, 6, 13) (dual of [(32775, 6), 196621, 14]-NRT-code) | [i] | ||
| 5 | Digital (16, 29, 32775)-net over F256 | [i] | ||