Information on Result #701740
Linear OA(283, 281, F2, 20) (dual of [281, 198, 21]-code), using construction XX applied to C1 = C([237,254]), C2 = C([241,2]), C3 = C1 + C2 = C([241,254]), and C∩ = C1 ∩ C2 = C([237,2]) based on
- linear OA(268, 255, F2, 18) (dual of [255, 187, 19]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−18,−17,…,−1}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(265, 255, F2, 17) (dual of [255, 190, 18]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−14,−13,…,2}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(277, 255, F2, 21) (dual of [255, 178, 22]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−18,−17,…,2}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(256, 255, F2, 14) (dual of [255, 199, 15]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−14,−13,…,−1}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- 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(284, 282, F2, 21) (dual of [282, 198, 22]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(283, 140, F2, 2, 20) (dual of [(140, 2), 197, 21]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(283, 70, F2, 4, 20) (dual of [(70, 4), 197, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(283, 56, F2, 5, 20) (dual of [(56, 5), 197, 21]-NRT-code) | [i] | ||