Information on Result #729344
Linear OA(32109, 1030, F32, 56) (dual of [1030, 921, 57]-code), using construction XX applied to C1 = C([1021,52]), C2 = C([0,53]), C3 = C1 + C2 = C([0,52]), and C∩ = C1 ∩ C2 = C([1021,53]) based on
- linear OA(32106, 1023, F32, 55) (dual of [1023, 917, 56]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(32104, 1023, F32, 54) (dual of [1023, 919, 55]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,53], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(32108, 1023, F32, 56) (dual of [1023, 915, 57]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,53}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(32102, 1023, F32, 53) (dual of [1023, 921, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [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(32109, 515, F32, 2, 56) (dual of [(515, 2), 921, 57]-NRT-code) | [i] | OOA Folding | |