Information on Result #2864917
Linear OOA(2146, 209720, F2, 5, 15) (dual of [(209720, 5), 1048454, 16]-NRT-code), using 22 times duplication based on linear OOA(2144, 209720, F2, 5, 15) (dual of [(209720, 5), 1048456, 16]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2144, 1048600, F2, 15) (dual of [1048600, 1048456, 16]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2142, 1048598, F2, 15) (dual of [1048598, 1048456, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2141, 1048576, F2, 15) (dual of [1048576, 1048435, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(14) ⊂ Ce(12) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2142, 1048598, F2, 15) (dual of [1048598, 1048456, 16]-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(2146, 209720, F2, 6, 15) (dual of [(209720, 6), 1258174, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2146, 209720, F2, 7, 15) (dual of [(209720, 7), 1467894, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(2146, 209720, F2, 8, 15) (dual of [(209720, 8), 1677614, 16]-NRT-code) | [i] | ||
| 4 | Digital (131, 146, 209720)-net over F2 | [i] | ||