Information on Result #729148
Linear OA(3279, 1030, F32, 41) (dual of [1030, 951, 42]-code), using construction XX applied to C1 = C([1021,37]), C2 = C([0,38]), C3 = C1 + C2 = C([0,37]), and C∩ = C1 ∩ C2 = C([1021,38]) based on
- linear OA(3276, 1023, F32, 40) (dual of [1023, 947, 41]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,37}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3274, 1023, F32, 39) (dual of [1023, 949, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3278, 1023, F32, 41) (dual of [1023, 945, 42]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3272, 1023, F32, 38) (dual of [1023, 951, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [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(8132, 1030, S8, 41) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1699, 1030, S16, 41) | [i] | ||
| 3 | Linear OA(32102, 1094, F32, 41) (dual of [1094, 992, 42]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(32104, 1106, F32, 41) (dual of [1106, 1002, 42]-code) | [i] | ||
| 5 | Linear OA(32106, 1128, F32, 41) (dual of [1128, 1022, 42]-code) | [i] | ||
| 6 | Linear OA(32108, 1134, F32, 41) (dual of [1134, 1026, 42]-code) | [i] | ||
| 7 | Linear OA(32110, 1150, F32, 41) (dual of [1150, 1040, 42]-code) | [i] | ||
| 8 | Linear OA(3286, 1053, F32, 41) (dual of [1053, 967, 42]-code) | [i] | Varšamov–Edel Lengthening | |
| 9 | Linear OA(3287, 1073, F32, 41) (dual of [1073, 986, 42]-code) | [i] | ||
| 10 | Linear OA(3288, 1110, F32, 41) (dual of [1110, 1022, 42]-code) | [i] | ||
| 11 | Linear OA(3289, 1173, F32, 41) (dual of [1173, 1084, 42]-code) | [i] | ||
| 12 | Linear OA(3290, 1263, F32, 41) (dual of [1263, 1173, 42]-code) | [i] | ||
| 13 | Linear OA(3291, 1372, F32, 41) (dual of [1372, 1281, 42]-code) | [i] | ||
| 14 | Linear OOA(3279, 515, F32, 2, 41) (dual of [(515, 2), 951, 42]-NRT-code) | [i] | OOA Folding | |