Information on Result #1699952
Linear OOA(2165, 52433, F2, 8, 18) (dual of [(52433, 8), 419299, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2165, 52433, F2, 5, 18) (dual of [(52433, 5), 262000, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2165, 262165, F2, 18) (dual of [262165, 262000, 19]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2163, 262163, F2, 18) (dual of [262163, 262000, 19]-code), using
- 1 times truncation [i] based on linear OA(2164, 262164, F2, 19) (dual of [262164, 262000, 20]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2163, 262144, F2, 19) (dual of [262144, 261981, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2145, 262144, F2, 17) (dual of [262144, 261999, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
- dual of repetition code with length 20 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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 X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- 1 times truncation [i] based on linear OA(2164, 262164, F2, 19) (dual of [262164, 262000, 20]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2163, 262163, F2, 18) (dual of [262163, 262000, 19]-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(2166, 52433, F2, 8, 18) (dual of [(52433, 8), 419298, 19]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2167, 52433, F2, 8, 18) (dual of [(52433, 8), 419297, 19]-NRT-code) | [i] | ||