Information on Result #894216
Linear OOA(2197, 4718588, F2, 2, 13) (dual of [(4718588, 2), 9436979, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(258, 524287, F2, 2, 6) (dual of [(524287, 2), 1048516, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F2, using
- 1 times m-reduction [i] based on digital (52, 59, 524287)-net over F2, using
- extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F2, 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
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(2197, 4718588, F2, 2, 12) (dual of [(4718588, 2), 9436979, 13]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2199, 4718589, F2, 2, 13) (dual of [(4718589, 2), 9436979, 14]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(2198, 4718588, F2, 2, 13) (dual of [(4718588, 2), 9436978, 14]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(2197, 3357835, F2, 3, 13) (dual of [(3357835, 3), 10073308, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2197, 3357835, F2, 4, 13) (dual of [(3357835, 4), 13431143, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(2197, 3357835, F2, 5, 13) (dual of [(3357835, 5), 16788978, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(2197, 3357835, F2, 6, 13) (dual of [(3357835, 6), 20146813, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(2197, 3357835, F2, 7, 13) (dual of [(3357835, 7), 23504648, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(2197, 3357835, F2, 8, 13) (dual of [(3357835, 8), 26862483, 14]-NRT-code) | [i] | ||
| 10 | Digital (184, 197, 3357835)-net over F2 | [i] | ||
| 11 | Linear OOA(2197, 2359294, F2, 4, 13) (dual of [(2359294, 4), 9436979, 14]-NRT-code) | [i] | OOA Folding | |