Information on Result #727971
Linear OA(3240, 1030, F32, 20) (dual of [1030, 990, 21]-code), using construction XX applied to C1 = C([1021,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([1021,17]) based on
- linear OA(3237, 1023, F32, 19) (dual of [1023, 986, 20]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3235, 1023, F32, 18) (dual of [1023, 988, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3239, 1023, F32, 20) (dual of [1023, 984, 21]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,17}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3233, 1023, F32, 17) (dual of [1023, 990, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-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 | OA(867, 1030, S8, 20) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1650, 1030, S16, 20) | [i] | ||
| 3 | Linear OA(3251, 1074, F32, 20) (dual of [1074, 1023, 21]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(3253, 1094, F32, 20) (dual of [1094, 1041, 21]-code) | [i] | ||
| 5 | Linear OA(3244, 1049, F32, 20) (dual of [1049, 1005, 21]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(3245, 1087, F32, 20) (dual of [1087, 1042, 21]-code) | [i] | ||
| 7 | Linear OA(3246, 1184, F32, 20) (dual of [1184, 1138, 21]-code) | [i] | ||
| 8 | Linear OOA(3240, 515, F32, 2, 20) (dual of [(515, 2), 990, 21]-NRT-code) | [i] | OOA Folding | |