Information on Result #894415
Linear OOA(2246, 4210693, F2, 2, 17) (dual of [(4210693, 2), 8421140, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(261, 16392, F2, 2, 8) (dual of [(16392, 2), 32723, 9]-NRT-code), using
- OOA 2-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 2-folding [i] based on linear OA(261, 32784, F2, 8) (dual of [32784, 32723, 9]-code), using
- linear OOA(2185, 4194301, F2, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-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(2246, 4210693, F2, 2, 16) (dual of [(4210693, 2), 8421140, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2248, 4210694, F2, 2, 17) (dual of [(4210694, 2), 8421140, 18]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(2247, 4210693, F2, 2, 17) (dual of [(4210693, 2), 8421139, 18]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(2246, 2105346, F2, 4, 17) (dual of [(2105346, 4), 8421138, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2246, 1403564, F2, 6, 17) (dual of [(1403564, 6), 8421138, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(2246, 1052673, F2, 8, 17) (dual of [(1052673, 8), 8421138, 18]-NRT-code) | [i] | ||