Information on Result #2417176
Linear OOA(263, 16393, F2, 2, 8) (dual of [(16393, 2), 32723, 9]-NRT-code), using strength reduction based on linear OOA(263, 16393, F2, 2, 9) (dual of [(16393, 2), 32723, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(263, 32786, F2, 9) (dual of [32786, 32723, 10]-code), using
- 1 times code embedding in larger space [i] based on linear OA(262, 32785, F2, 9) (dual of [32785, 32723, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(261, 32768, F2, 9) (dual of [32768, 32707, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(246, 32768, F2, 7) (dual of [32768, 32722, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(216, 17, F2, 15) (dual of [17, 1, 16]-code), using
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- dual of repetition code with length 17 [i]
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- linear OA(21, 17, F2, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(262, 32785, F2, 9) (dual of [32785, 32723, 10]-code), 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(263, 12251, F2, 3, 8) (dual of [(12251, 3), 36690, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(263, 12251, F2, 4, 8) (dual of [(12251, 4), 48941, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(263, 12251, F2, 5, 8) (dual of [(12251, 5), 61192, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(263, 12251, F2, 6, 8) (dual of [(12251, 6), 73443, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(263, 12251, F2, 7, 8) (dual of [(12251, 7), 85694, 9]-NRT-code) | [i] | ||