Information on Result #702023
Linear OA(2179, 270, F2, 54) (dual of [270, 91, 55]-code), using construction XX applied to C1 = C([253,50]), C2 = C([1,52]), C3 = C1 + C2 = C([1,50]), and C∩ = C1 ∩ C2 = C([253,52]) based on
- linear OA(2173, 255, F2, 53) (dual of [255, 82, 54]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2168, 255, F2, 52) (dual of [255, 87, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2177, 255, F2, 55) (dual of [255, 78, 56]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- 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(21, 10, F2, 1) (dual of [10, 9, 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
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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 (see above)
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(2184, 275, F2, 54) (dual of [275, 91, 55]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2185, 276, F2, 54) (dual of [276, 91, 55]-code) | [i] | ||
| 3 | Linear OA(2180, 271, F2, 55) (dual of [271, 91, 56]-code) | [i] | Adding a Parity Check Bit | |
| 4 | Linear OA(2184, 276, F2, 54) (dual of [276, 92, 55]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(2179, 135, F2, 2, 54) (dual of [(135, 2), 91, 55]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2179, 90, F2, 3, 54) (dual of [(90, 3), 91, 55]-NRT-code) | [i] | ||