Information on Result #729181
Linear OA(3283, 1030, F32, 43) (dual of [1030, 947, 44]-code), using construction XX applied to C1 = C([1021,39]), C2 = C([0,40]), C3 = C1 + C2 = C([0,39]), and C∩ = C1 ∩ C2 = C([1021,40]) based on
- linear OA(3280, 1023, F32, 42) (dual of [1023, 943, 43]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,39}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3278, 1023, F32, 41) (dual of [1023, 945, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3282, 1023, F32, 43) (dual of [1023, 941, 44]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,40}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3276, 1023, F32, 40) (dual of [1023, 947, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [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(8139, 1030, S8, 43) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(16104, 1030, S16, 43) | [i] | ||
| 3 | Linear OA(32107, 1094, F32, 43) (dual of [1094, 987, 44]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(32109, 1106, F32, 43) (dual of [1106, 997, 44]-code) | [i] | ||
| 5 | Linear OA(3290, 1054, F32, 43) (dual of [1054, 964, 44]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(3291, 1076, F32, 43) (dual of [1076, 985, 44]-code) | [i] | ||
| 7 | Linear OA(3293, 1180, F32, 43) (dual of [1180, 1087, 44]-code) | [i] | ||
| 8 | Linear OOA(3283, 515, F32, 2, 43) (dual of [(515, 2), 947, 44]-NRT-code) | [i] | OOA Folding | |