Information on Result #702171
Linear OA(2249, 589, F2, 52) (dual of [589, 340, 53]-code), using construction X applied to C([1,52]) ⊂ C([1,40]) based on
- linear OA(2216, 511, F2, 52) (dual of [511, 295, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2171, 511, F2, 40) (dual of [511, 340, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(2253, 593, F2, 52) (dual of [593, 340, 53]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2254, 594, F2, 52) (dual of [594, 340, 53]-code) | [i] | ||
| 3 | Linear OA(2250, 590, F2, 53) (dual of [590, 340, 54]-code) | [i] | Adding a Parity Check Bit | |
| 4 | Linear OOA(2249, 294, F2, 2, 52) (dual of [(294, 2), 339, 53]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2249, 196, F2, 3, 52) (dual of [(196, 3), 339, 53]-NRT-code) | [i] | ||