Information on Result #1816104
OA(16115, 1051, S16, 44), using discarding parts of the base based on linear OA(3292, 1051, F32, 44) (dual of [1051, 959, 45]-code), using
- construction XX applied to C1 = C([1014,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([1014,34]) [i] based on
- linear OA(3282, 1023, F32, 43) (dual of [1023, 941, 44]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−9,−8,…,33}, and designed minimum distance d ≥ |I|+1 = 44 [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(3284, 1023, F32, 44) (dual of [1023, 939, 45]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−9,−8,…,34}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- 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(328, 26, F32, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,32)), using
- discarding factors / shortening the dual code based on linear OA(328, 32, F32, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
- Reed–Solomon code RS(24,32) [i]
- discarding factors / shortening the dual code based on linear OA(328, 32, F32, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), 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.
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(16116, 1052, S16, 44) | [i] | Code Embedding in Larger Space | |
| 2 | OA(16117, 1053, S16, 44) | [i] | ||