Information on Result #2258740
Linear OA(2183, 262164, F2, 21) (dual of [262164, 261981, 22]-code), using 1 times code embedding in larger space based on linear OA(2182, 262163, F2, 21) (dual of [262163, 261981, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2181, 262144, F2, 21) (dual of [262144, 261963, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(21, 19, F2, 1) (dual of [19, 18, 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
Mode: Constructive and 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(2183, 131082, F2, 2, 21) (dual of [(131082, 2), 261981, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2183, 87388, F2, 3, 21) (dual of [(87388, 3), 261981, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(2183, 65541, F2, 4, 21) (dual of [(65541, 4), 261981, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2183, 43694, F2, 6, 21) (dual of [(43694, 6), 261981, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(2183, 37452, F2, 7, 21) (dual of [(37452, 7), 261981, 22]-NRT-code) | [i] | ||