Information on Result #945170
Linear OOA(2103, 349533, F2, 3, 10) (dual of [(349533, 3), 1048496, 11]-NRT-code), using OOA 3-folding based on linear OA(2103, 1048599, F2, 10) (dual of [1048599, 1048496, 11]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2101, 1048597, F2, 10) (dual of [1048597, 1048496, 11]-code), using
- 1 times truncation [i] based on linear OA(2102, 1048598, F2, 11) (dual of [1048598, 1048496, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- 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(281, 1048576, F2, 9) (dual of [1048576, 1048495, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(10) ⊂ Ce(8) [i] based on
- 1 times truncation [i] based on linear OA(2102, 1048598, F2, 11) (dual of [1048598, 1048496, 12]-code), 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(2104, 349533, F2, 3, 10) (dual of [(349533, 3), 1048495, 11]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2103, 311442, F2, 4, 10) (dual of [(311442, 4), 1245665, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2103, 311442, F2, 5, 10) (dual of [(311442, 5), 1557107, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(2103, 311442, F2, 6, 10) (dual of [(311442, 6), 1868549, 11]-NRT-code) | [i] | ||
| 5 | Linear OOA(2103, 311442, F2, 7, 10) (dual of [(311442, 7), 2179991, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(2103, 311442, F2, 8, 10) (dual of [(311442, 8), 2491433, 11]-NRT-code) | [i] | ||
| 7 | Digital (93, 103, 311442)-net over F2 | [i] | ||