Information on Result #727831
Linear OA(3231, 1027, F32, 16) (dual of [1027, 996, 17]-code), using construction XX applied to C1 = C([1022,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([1022,14]) based on
- linear OA(3229, 1023, F32, 15) (dual of [1023, 994, 16]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3229, 1023, F32, 15) (dual of [1023, 994, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3231, 1023, F32, 16) (dual of [1023, 992, 17]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3227, 1023, F32, 14) (dual of [1023, 996, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [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(852, 1027, S8, 16) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1639, 1027, S16, 16) | [i] | ||
| 3 | Linear OA(3239, 1060, F32, 16) (dual of [1060, 1021, 17]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(3240, 1071, F32, 16) (dual of [1071, 1031, 17]-code) | [i] | ||
| 5 | Linear OA(3241, 1073, F32, 16) (dual of [1073, 1032, 17]-code) | [i] | ||
| 6 | Linear OA(3242, 1091, F32, 16) (dual of [1091, 1049, 17]-code) | [i] | ||
| 7 | Linear OA(3243, 1093, F32, 16) (dual of [1093, 1050, 17]-code) | [i] | ||
| 8 | Linear OA(3244, 1123, F32, 16) (dual of [1123, 1079, 17]-code) | [i] | ||
| 9 | Linear OA(3245, 1126, F32, 16) (dual of [1126, 1081, 17]-code) | [i] | ||
| 10 | Linear OA(3235, 1044, F32, 16) (dual of [1044, 1009, 17]-code) | [i] | Varšamov–Edel Lengthening | |
| 11 | Linear OA(3236, 1078, F32, 16) (dual of [1078, 1042, 17]-code) | [i] | ||
| 12 | Linear OA(3237, 1172, F32, 16) (dual of [1172, 1135, 17]-code) | [i] | ||
| 13 | Linear OA(3238, 1378, F32, 16) (dual of [1378, 1340, 17]-code) | [i] | ||
| 14 | Linear OA(3239, 1708, F32, 16) (dual of [1708, 1669, 17]-code) | [i] | ||