Information on Result #869052
Linear OOA(3212, 515, F32, 2, 6) (dual of [(515, 2), 1018, 7]-NRT-code), using OOA 2-folding based on linear OA(3212, 1030, F32, 6) (dual of [1030, 1018, 7]-code), using
- construction XX applied to C1 = C([1021,2]), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([1021,3]) [i] based on
- linear OA(329, 1023, F32, 5) (dual of [1023, 1014, 6]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(327, 1023, F32, 4) (dual of [1023, 1016, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(3211, 1023, F32, 6) (dual of [1023, 1012, 7]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,3}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(325, 1023, F32, 3) (dual of [1023, 1018, 4]-code or 1023-cap in PG(4,32)), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), 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 | Linear OOA(3268, 4194816, F32, 2, 12) (dual of [(4194816, 2), 8389564, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3273, 4194816, F32, 2, 13) (dual of [(4194816, 2), 8389559, 14]-NRT-code) | [i] | ||
| 3 | OOA(3266, 4194816, S32, 2, 12) | [i] | ||
| 4 | OOA(3271, 4194816, S32, 2, 13) | [i] | ||