Information on Result #1631760
Linear OOA(2124, 2397, F2, 5, 18) (dual of [(2397, 5), 11861, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2124, 2397, F2, 3, 18) (dual of [(2397, 3), 7067, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2124, 2741, F2, 3, 18) (dual of [(2741, 3), 8099, 19]-NRT-code), using
- strength reduction [i] based on linear OOA(2124, 2741, F2, 3, 19) (dual of [(2741, 3), 8099, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2124, 8223, F2, 19) (dual of [8223, 8099, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2124, 8224, F2, 19) (dual of [8224, 8100, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2118, 8192, F2, 19) (dual of [8192, 8074, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(292, 8192, F2, 15) (dual of [8192, 8100, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2124, 8224, F2, 19) (dual of [8224, 8100, 20]-code), using
- OOA 3-folding [i] based on linear OA(2124, 8223, F2, 19) (dual of [8223, 8099, 20]-code), using
- strength reduction [i] based on linear OOA(2124, 2741, F2, 3, 19) (dual of [(2741, 3), 8099, 20]-NRT-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(2124, 1198, F2, 25, 18) (dual of [(1198, 25), 29826, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |