Information on Result #728175
Linear OA(3275, 1062, F32, 32) (dual of [1062, 987, 33]-code), using construction XX applied to C1 = C([4,32]), C2 = C([1,20]), C3 = C1 + C2 = C([4,20]), and C∩ = C1 ∩ C2 = C([1,32]) based on
- linear OA(3258, 1023, F32, 29) (dual of [1023, 965, 30]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {4,5,…,32}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3240, 1023, F32, 20) (dual of [1023, 983, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3262, 1023, F32, 32) (dual of [1023, 961, 33]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3234, 1023, F32, 17) (dual of [1023, 989, 18]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {4,5,…,20}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(3211, 33, F32, 11) (dual of [33, 22, 12]-code or 33-arc in PG(10,32)), using
- extended Reed–Solomon code RSe(22,32) [i]
- the expurgated narrow-sense BCH-code C(I) with length 33 | 322−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(322, 6, F32, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), 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(3275, 531, F32, 2, 32) (dual of [(531, 2), 987, 33]-NRT-code) | [i] | OOA Folding | |