Information on Result #701996
Linear OA(2171, 280, F2, 49) (dual of [280, 109, 50]-code), using construction XX applied to C1 = C([251,42]), C2 = C([0,44]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([251,44]) 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 = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2149, 255, F2, 45) (dual of [255, 106, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2165, 255, F2, 49) (dual of [255, 90, 50]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2141, 255, F2, 43) (dual of [255, 114, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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(2170, 279, F2, 48) (dual of [279, 109, 49]-code) | [i] | Truncation | |
| 2 | Linear OOA(2171, 140, F2, 2, 49) (dual of [(140, 2), 109, 50]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2171, 93, F2, 3, 49) (dual of [(93, 3), 108, 50]-NRT-code) | [i] | ||