Information on Result #729170
Linear OA(3293, 1042, F32, 46) (dual of [1042, 949, 47]-code), using construction XX applied to C1 = C([1017,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([1017,39]) based on
- linear OA(3286, 1023, F32, 45) (dual of [1023, 937, 46]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−6,−5,…,38}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3276, 1023, F32, 40) (dual of [1023, 947, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3288, 1023, F32, 46) (dual of [1023, 935, 47]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−6,−5,…,39}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3274, 1023, F32, 39) (dual of [1023, 949, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), 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(8155, 1042, S8, 46) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(16117, 1042, S16, 46) | [i] | ||
| 3 | Linear OOA(3293, 521, F32, 2, 46) (dual of [(521, 2), 949, 47]-NRT-code) | [i] | OOA Folding | |