Information on Result #1664596
Linear OOA(2145, 2097155, F2, 6, 12) (dual of [(2097155, 6), 12582785, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2145, 2097155, F2, 4, 12) (dual of [(2097155, 4), 8388475, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(27, 5, F2, 4, 6) (dual of [(5, 4), 13, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(4;F,13P) [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- linear OOA(2138, 2097150, F2, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OOA 4-folding [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- linear OOA(27, 5, F2, 4, 6) (dual of [(5, 4), 13, 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(2145, 2097154, F2, 7, 12) (dual of [(2097154, 7), 14679933, 13]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(2145, 2097154, F2, 8, 12) (dual of [(2097154, 8), 16777087, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2145, 2097154, F2, 18, 12) (dual of [(2097154, 18), 37748627, 13]-NRT-code) | [i] | ||