Information on Result #2667048
Linear OOA(2248, 2807129, F2, 3, 17) (dual of [(2807129, 3), 8421139, 18]-NRT-code), using 22 times duplication based on linear OOA(2246, 2807129, F2, 3, 17) (dual of [(2807129, 3), 8421141, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(261, 10928, F2, 3, 8) (dual of [(10928, 3), 32723, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(261, 32784, F2, 8) (dual of [32784, 32723, 9]-code), using
- 1 times truncation [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 truncation [i] based on linear OA(262, 32785, F2, 9) (dual of [32785, 32723, 10]-code), using
- OOA 3-folding [i] based on linear OA(261, 32784, F2, 8) (dual of [32784, 32723, 9]-code), using
- linear OOA(2185, 2796201, F2, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- linear OOA(261, 10928, F2, 3, 8) (dual of [(10928, 3), 32723, 9]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2248, 2670919, F2, 4, 17) (dual of [(2670919, 4), 10683428, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2248, 2670919, F2, 5, 17) (dual of [(2670919, 5), 13354347, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(2248, 2670919, F2, 6, 17) (dual of [(2670919, 6), 16025266, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(2248, 2670919, F2, 7, 17) (dual of [(2670919, 7), 18696185, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(2248, 2670919, F2, 8, 17) (dual of [(2670919, 8), 21367104, 18]-NRT-code) | [i] | ||
| 6 | Digital (231, 248, 2670919)-net over F2 | [i] | ||