Information on Result #1699779
Linear OOA(2162, 174766, F2, 8, 17) (dual of [(174766, 8), 1397966, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2162, 174766, F2, 6, 17) (dual of [(174766, 6), 1048434, 18]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2162, 1048596, F2, 17) (dual of [1048596, 1048434, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, 1048597, F2, 17) (dual of [1048597, 1048435, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2161, 1048576, F2, 17) (dual of [1048576, 1048415, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2141, 1048576, F2, 15) (dual of [1048576, 1048435, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 21, F2, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2162, 1048597, F2, 17) (dual of [1048597, 1048435, 18]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2163, 174766, F2, 8, 17) (dual of [(174766, 8), 1397965, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2164, 174766, F2, 8, 17) (dual of [(174766, 8), 1397964, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(2165, 174766, F2, 8, 17) (dual of [(174766, 8), 1397963, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(2162, 174765, F2, 24, 17) (dual of [(174765, 24), 4194198, 18]-NRT-code) | [i] | OOA Stacking with Additional Row | |