Information on Result #729277
Linear OA(32104, 1039, F32, 52) (dual of [1039, 935, 53]-code), using construction XX applied to C1 = C([1018,45]), C2 = C([0,46]), C3 = C1 + C2 = C([0,45]), and C∩ = C1 ∩ C2 = C([1018,46]) based on
- linear OA(3298, 1023, F32, 51) (dual of [1023, 925, 52]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−5,−4,…,45}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(3290, 1023, F32, 47) (dual of [1023, 933, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(32100, 1023, F32, 52) (dual of [1023, 923, 53]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−5,−4,…,46}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(3288, 1023, F32, 46) (dual of [1023, 935, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(324, 14, F32, 4) (dual of [14, 10, 5]-code or 14-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(16130, 1039, S16, 52) | [i] | Discarding Parts of the Base for OAs | |