Information on Result #727653
Linear OA(3217, 1027, F32, 9) (dual of [1027, 1010, 10]-code), using construction XX applied to C1 = C([1022,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([1022,7]) based on
- linear OA(3215, 1023, F32, 8) (dual of [1023, 1008, 9]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(3215, 1023, F32, 8) (dual of [1023, 1008, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(3217, 1023, F32, 9) (dual of [1023, 1006, 10]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3213, 1023, F32, 7) (dual of [1023, 1010, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
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(1622, 1027, S16, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(3254, 2054, F32, 19) (dual of [2054, 2000, 20]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(3272, 33798, F32, 19) (dual of [33798, 33726, 20]-code) | [i] | ||
| 4 | Linear OA(3290, 1049607, F32, 19) (dual of [1049607, 1049517, 20]-code) | [i] | ||
| 5 | Linear OA(3221, 1060, F32, 9) (dual of [1060, 1039, 10]-code) | [i] | ||
| 6 | Linear OA(3222, 1071, F32, 9) (dual of [1071, 1049, 10]-code) | [i] | ||
| 7 | Linear OA(3223, 2019, F32, 9) (dual of [2019, 1996, 10]-code) | [i] | ||
| 8 | Linear OA(3224, 2054, F32, 9) (dual of [2054, 2030, 10]-code) | [i] | ||
| 9 | Linear OA(3219, 1035, F32, 9) (dual of [1035, 1016, 10]-code) | [i] | Varšamov–Edel Lengthening | |
| 10 | Linear OA(3220, 1069, F32, 9) (dual of [1069, 1049, 10]-code) | [i] | ||
| 11 | Linear OA(3221, 1227, F32, 9) (dual of [1227, 1206, 10]-code) | [i] | ||
| 12 | Linear OA(3222, 1701, F32, 9) (dual of [1701, 1679, 10]-code) | [i] | ||
| 13 | Linear OA(3223, 2587, F32, 9) (dual of [2587, 2564, 10]-code) | [i] | ||