Information on Result #702009
Linear OA(2175, 281, F2, 51) (dual of [281, 106, 52]-code), using construction XX applied to C1 = C([217,8]), C2 = C([213,4]), C3 = C1 + C2 = C([217,4]), and C∩ = C1 ∩ C2 = C([213,8]) based on
- linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−38,−37,…,8}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−42,−41,…,4}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2165, 255, F2, 51) (dual of [255, 90, 52]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−42,−41,…,8}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2149, 255, F2, 43) (dual of [255, 106, 44]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−38,−37,…,4}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(25, 13, F2, 3) (dual of [13, 8, 4]-code or 13-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
- linear OA(25, 13, F2, 3) (dual of [13, 8, 4]-code or 13-cap in PG(4,2)) (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(2174, 280, F2, 50) (dual of [280, 106, 51]-code) | [i] | Truncation | |
| 2 | Linear OOA(2175, 140, F2, 2, 51) (dual of [(140, 2), 105, 52]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2175, 93, F2, 3, 51) (dual of [(93, 3), 104, 52]-NRT-code) | [i] | ||