Information on Result #1838825
OOA(12870, 16641, S128, 4, 25), using (u, u+v)-construction based on
- OOA(12814, 257, S128, 4, 12), using
- extracting embedded OOA [i] based on (2, 14, 257)-net in base 128, using
- 2 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- 2 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- extracting embedded OOA [i] based on (2, 14, 257)-net in base 128, using
- OOA(12856, 16384, S128, 4, 25), using
- OOA 4-folding [i] based on OA(12856, 65536, S128, 25), using
- discarding factors based on OA(12856, 65538, S128, 25), using
- discarding parts of the base [i] based on linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- discarding factors based on OA(12856, 65538, S128, 25), using
- OOA 4-folding [i] based on OA(12856, 65536, S128, 25), 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(12870, 5546, S128, 28, 25) | [i] | OOA Folding and Stacking with Additional Row | |