Information on Result #1831893
OOA(27109, 9961, S27, 2, 30), using (u, u+v)-construction based on
- OOA(2723, 116, S27, 2, 15), using
- extracting embedded OOA [i] based on (8, 23, 116)-net in base 27, using
- 1 times m-reduction [i] based on (8, 24, 116)-net in base 27, using
- base change [i] based on digital (2, 18, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 18, 116)-net over F81, using
- 1 times m-reduction [i] based on (8, 24, 116)-net in base 27, using
- extracting embedded OOA [i] based on (8, 23, 116)-net in base 27, using
- linear OOA(2786, 9845, F27, 2, 30) (dual of [(9845, 2), 19604, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2786, 19690, F27, 30) (dual of [19690, 19604, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- OOA 2-folding [i] based on linear OA(2786, 19690, F27, 30) (dual of [19690, 19604, 31]-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(27110, 9961, S27, 2, 30) | [i] | OOA Duplication | |