Information on Result #1664743
Linear OOA(2148, 1677729, F2, 6, 13) (dual of [(1677729, 6), 10066226, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2148, 1677729, F2, 5, 13) (dual of [(1677729, 5), 8388497, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(29, 9, F2, 5, 6) (dual of [(9, 5), 36, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (3, 9, 9)-net over F2, using
- linear OOA(2139, 1677720, F2, 5, 13) (dual of [(1677720, 5), 8388461, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 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 5-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 14]-code), using
- linear OOA(29, 9, F2, 5, 6) (dual of [(9, 5), 36, 7]-NRT-code), using
Mode: 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(2148, 1677728, F2, 7, 13) (dual of [(1677728, 7), 11743948, 14]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(2148, 1677728, F2, 8, 13) (dual of [(1677728, 8), 13421676, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(2148, 1677728, F2, 18, 13) (dual of [(1677728, 18), 30198956, 14]-NRT-code) | [i] | ||