Information on Result #1516053
Linear OOA(2211, large, F2, 3, 13), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2211, large, F2, 2, 13), using
- 21 times duplication [i] based on linear OOA(2210, large, F2, 2, 13), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2206, 8388602, F2, 2, 13) (dual of [(8388602, 2), 16776998, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(267, 4194303, F2, 2, 6) (dual of [(4194303, 2), 8388539, 7]-NRT-code), using
- linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- (u, u+v)-construction [i] based on
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2206, 8388602, F2, 2, 13) (dual of [(8388602, 2), 16776998, 14]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and t, 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(2211, large, F2, 3, 12) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2214, large, F2, 3, 13) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(2217, large, F2, 3, 13) | [i] | ||
| 4 | Linear OOA(2220, large, F2, 3, 13) | [i] | ||
| 5 | Linear OOA(2223, large, F2, 3, 13) | [i] | ||
| 6 | Linear OOA(2226, large, F2, 3, 13) | [i] | ||
| 7 | Linear OOA(2229, large, F2, 3, 13) | [i] | ||
| 8 | Linear OOA(2232, large, F2, 3, 13) | [i] | ||
| 9 | Linear OOA(2235, large, F2, 3, 13) | [i] | ||
| 10 | Linear OOA(2238, large, F2, 3, 13) | [i] | ||
| 11 | Linear OOA(2241, large, F2, 3, 13) | [i] | ||
| 12 | Linear OOA(2244, large, F2, 3, 13) | [i] | ||
| 13 | Linear OOA(2247, large, F2, 3, 13) | [i] | ||
| 14 | Linear OOA(2253, large, F2, 3, 13) | [i] | ||
| 15 | Linear OOA(2256, large, F2, 3, 13) | [i] | ||
| 16 | Linear OOA(2259, large, F2, 3, 13) | [i] | ||
| 17 | Linear OOA(2212, large, F2, 3, 13) | [i] | OOA Duplication | |
| 18 | Linear OOA(2213, large, F2, 3, 13) | [i] | ||
| 19 | Linear OOA(2211, 4194301, F2, 5, 13) (dual of [(4194301, 5), 20971294, 14]-NRT-code) | [i] | OOA Folding | |
| 20 | Linear OOA(2211, 4194301, F2, 6, 13) (dual of [(4194301, 6), 25165595, 14]-NRT-code) | [i] | ||