Information on Result #701922
Linear OA(2154, 289, F2, 40) (dual of [289, 135, 41]-code), using construction XX applied to C1 = C([217,254]), C2 = C([225,2]), C3 = C1 + C2 = C([225,254]), and C∩ = C1 ∩ C2 = C([217,2]) based on
- linear OA(2132, 255, F2, 38) (dual of [255, 123, 39]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−38,−37,…,−1}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2125, 255, F2, 33) (dual of [255, 130, 34]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−30,−29,…,2}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2141, 255, F2, 41) (dual of [255, 114, 42]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−38,−37,…,2}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2116, 255, F2, 30) (dual of [255, 139, 31]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−30,−29,…,−1}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- extended Golay code Ge(2) [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
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(2155, 290, F2, 41) (dual of [290, 135, 42]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2154, 144, F2, 2, 40) (dual of [(144, 2), 134, 41]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2154, 96, F2, 3, 40) (dual of [(96, 3), 134, 41]-NRT-code) | [i] | ||