Information on Result #1095290
Linear OOA(2122, 209719, F2, 5, 13) (dual of [(209719, 5), 1048473, 14]-NRT-code), using OOA 5-folding based on linear OA(2122, 1048595, F2, 13) (dual of [1048595, 1048473, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2122, 1048597, F2, 13) (dual of [1048597, 1048475, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2121, 1048576, F2, 13) (dual of [1048576, 1048455, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2101, 1048576, F2, 11) (dual of [1048576, 1048475, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(12) ⊂ Ce(10) [i] based on
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(2122, 209719, F2, 5, 12) (dual of [(209719, 5), 1048473, 13]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2123, 209719, F2, 5, 13) (dual of [(209719, 5), 1048472, 14]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2122, 209719, F2, 6, 13) (dual of [(209719, 6), 1258192, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2122, 209719, F2, 7, 13) (dual of [(209719, 7), 1467911, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(2122, 209719, F2, 8, 13) (dual of [(209719, 8), 1677630, 14]-NRT-code) | [i] | ||
| 6 | Digital (109, 122, 209719)-net over F2 | [i] | ||