Information on Result #1051316
Linear OOA(2104, 262150, F2, 4, 11) (dual of [(262150, 4), 1048496, 12]-NRT-code), using OOA 4-folding based on linear OA(2104, 1048600, F2, 11) (dual of [1048600, 1048496, 12]-code), using
- 2 times code embedding in larger space [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
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(2105, 262150, F2, 4, 11) (dual of [(262150, 4), 1048495, 12]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2103, 262149, F2, 4, 10) (dual of [(262149, 4), 1048493, 11]-NRT-code) | [i] | Truncation for OOAs | |
| 3 | Linear OOA(2104, 262150, F2, 5, 11) (dual of [(262150, 5), 1310646, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2104, 262150, F2, 6, 11) (dual of [(262150, 6), 1572796, 12]-NRT-code) | [i] | ||
| 5 | Linear OOA(2104, 262150, F2, 7, 11) (dual of [(262150, 7), 1834946, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(2104, 262150, F2, 8, 11) (dual of [(262150, 8), 2097096, 12]-NRT-code) | [i] | ||
| 7 | Digital (93, 104, 262150)-net over F2 | [i] | ||