Information on Result #728558
Linear OA(3272, 1042, F32, 35) (dual of [1042, 970, 36]-code), using construction XX applied to C1 = C([0,33]), C2 = C([7,34]), C3 = C1 + C2 = C([7,33]), 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(3255, 1023, F32, 28) (dual of [1023, 968, 29]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {7,8,…,34}, and designed minimum distance d ≥ |I|+1 = 29 [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(3253, 1023, F32, 27) (dual of [1023, 970, 28]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {7,8,…,33}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(326, 17, F32, 6) (dual of [17, 11, 7]-code or 17-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), 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(8120, 1042, S8, 35) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1690, 1042, S16, 35) | [i] | ||
| 3 | Linear OOA(3272, 521, F32, 2, 35) (dual of [(521, 2), 970, 36]-NRT-code) | [i] | OOA Folding | |