Information on Result #728694
Linear OA(3270, 1036, F32, 35) (dual of [1036, 966, 36]-code), using construction XX applied to C1 = C([0,33]), C2 = C([5,34]), C3 = C1 + C2 = C([5,33]), and C∩ = C1 ∩ C2 = C([0,34]) based on
- linear OA(3264, 1023, F32, 34) (dual of [1023, 959, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3259, 1023, F32, 30) (dual of [1023, 964, 31]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {5,6,…,34}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3266, 1023, F32, 35) (dual of [1023, 957, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3257, 1023, F32, 29) (dual of [1023, 966, 30]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {5,6,…,33}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(324, 11, F32, 4) (dual of [11, 7, 5]-code or 11-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), 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(8117, 1036, S8, 35) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1688, 1036, S16, 35) | [i] | ||
| 3 | Linear OOA(3270, 518, F32, 2, 35) (dual of [(518, 2), 966, 36]-NRT-code) | [i] | OOA Folding | |