Information on Result #1584301
Linear OOA(241, 1048597, F2, 4, 4) (dual of [(1048597, 4), 4194347, 5]-NRT-code), using appending kth column based on linear OOA(241, 1048597, F2, 3, 4) (dual of [(1048597, 3), 3145750, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(241, 1048597, F2, 4) (dual of [1048597, 1048556, 5]-code), using
- 1 times truncation [i] based on linear OA(242, 1048598, F2, 5) (dual of [1048598, 1048556, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(241, 1048576, F2, 5) (dual of [1048576, 1048535, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(221, 1048576, F2, 3) (dual of [1048576, 1048555, 4]-code or 1048576-cap in PG(20,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(221, 22, F2, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
- dual of repetition code with length 22 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 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(4) ⊂ Ce(2) [i] based on
- 1 times truncation [i] based on linear OA(242, 1048598, F2, 5) (dual of [1048598, 1048556, 6]-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(241, 1048597, F2, 5, 4) (dual of [(1048597, 5), 5242944, 5]-NRT-code) | [i] | Appending Arbitrary Columns | |
| 2 | Linear OOA(241, 1048597, F2, 6, 4) (dual of [(1048597, 6), 6291541, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(241, 1048597, F2, 7, 4) (dual of [(1048597, 7), 7340138, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(241, 1048597, F2, 8, 4) (dual of [(1048597, 8), 8388735, 5]-NRT-code) | [i] | ||
| 5 | Digital (37, 41, 1048597)-net over F2 | [i] | Net Defined by OOA | |