Information on Result #727712
Linear OA(3223, 1027, F32, 12) (dual of [1027, 1004, 13]-code), using construction XX applied to C1 = C([1022,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([1022,10]) based on
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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(839, 1027, S8, 12) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1629, 1027, S16, 12) | [i] | ||
| 3 | Linear OA(3272, 2054, F32, 25) (dual of [2054, 1982, 26]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(3296, 33798, F32, 25) (dual of [33798, 33702, 26]-code) | [i] | ||
| 5 | Linear OA(3229, 1060, F32, 12) (dual of [1060, 1031, 13]-code) | [i] | ||
| 6 | Linear OA(3230, 1071, F32, 12) (dual of [1071, 1041, 13]-code) | [i] | ||
| 7 | Linear OA(3231, 1073, F32, 12) (dual of [1073, 1042, 13]-code) | [i] | ||
| 8 | Linear OA(3232, 1093, F32, 12) (dual of [1093, 1061, 13]-code) | [i] | ||
| 9 | Linear OA(3233, 1124, F32, 12) (dual of [1124, 1091, 13]-code) | [i] | ||
| 10 | Linear OA(3227, 1069, F32, 12) (dual of [1069, 1042, 13]-code) | [i] | Varšamov–Edel Lengthening | |
| 11 | Linear OA(3228, 1196, F32, 12) (dual of [1196, 1168, 13]-code) | [i] | ||
| 12 | Linear OA(3229, 1505, F32, 12) (dual of [1505, 1476, 13]-code) | [i] | ||
| 13 | Linear OA(3230, 2026, F32, 12) (dual of [2026, 1996, 13]-code) | [i] | ||