Information on Result #701658
Linear OA(2176, 291, F2, 48) (dual of [291, 115, 49]-code), using construction X applied to C([1,50]) ⊂ C([1,42]) based on
- linear OA(2164, 255, F2, 50) (dual of [255, 91, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2140, 255, F2, 42) (dual of [255, 115, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(212, 36, F2, 5) (dual of [36, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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 X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-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 OA(2177, 292, F2, 49) (dual of [292, 115, 50]-code) | [i] | Adding a Parity Check Bit | |