Information on Result #727771
Linear OA(3233, 1033, F32, 16) (dual of [1033, 1000, 17]-code), using construction XX applied to C1 = C([1020,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([1020,12]) 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 = {−3,−2,…,11}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3225, 1023, F32, 13) (dual of [1023, 998, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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 = {−3,−2,…,12}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), 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(855, 1033, S8, 16) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1642, 1033, S16, 16) | [i] | ||