Information on Result #702165
Linear OA(2240, 589, F2, 50) (dual of [589, 349, 51]-code), using construction X applied to C([1,50]) ⊂ C([1,38]) based on
- linear OA(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2162, 511, F2, 38) (dual of [511, 349, 39]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(233, 78, F2, 11) (dual of [78, 45, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- linear OA(228, 64, F2, 11) (dual of [64, 36, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(219, 64, F2, 7) (dual of [64, 45, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- construction X applied to Ce(10) ⊂ Ce(6) [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 OA(2244, 593, F2, 50) (dual of [593, 349, 51]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2241, 590, F2, 51) (dual of [590, 349, 52]-code) | [i] | Adding a Parity Check Bit | |
| 3 | Linear OOA(2240, 294, F2, 2, 50) (dual of [(294, 2), 348, 51]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2240, 196, F2, 3, 50) (dual of [(196, 3), 348, 51]-NRT-code) | [i] | ||