Information on Result #1665325
Linear OOA(2159, 2097229, F2, 6, 13) (dual of [(2097229, 6), 12583215, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2159, 2097229, F2, 4, 13) (dual of [(2097229, 4), 8388757, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(220, 79, F2, 4, 6) (dual of [(79, 4), 296, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (14, 20, 79)-net over F2, using
- linear OOA(2139, 2097150, F2, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
- OOA 4-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 4-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 14]-code), using
- linear OOA(220, 79, F2, 4, 6) (dual of [(79, 4), 296, 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(2159, 2097228, F2, 7, 13) (dual of [(2097228, 7), 14680437, 14]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(2159, 2097228, F2, 8, 13) (dual of [(2097228, 8), 16777665, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(2159, 2097228, F2, 18, 13) (dual of [(2097228, 18), 37749945, 14]-NRT-code) | [i] | ||