Information on Result #725097
Linear OA(2732, 110, F27, 18) (dual of [110, 78, 19]-code), using construction XX applied to C1 = C([0,16]), C2 = C([2,17]), C3 = C1 + C2 = C([2,16]), and C∩ = C1 ∩ C2 = C([0,17]) based on
- linear OA(2729, 104, F27, 17) (dual of [104, 75, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2728, 104, F27, 16) (dual of [104, 76, 17]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {2,3,…,17}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2731, 104, F27, 18) (dual of [104, 73, 19]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2726, 104, F27, 15) (dual of [104, 78, 16]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {2,3,…,16}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(271, 4, F27, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- Reed–Solomon code RS(26,27) [i]
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 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 OA(27102, 842, F27, 37) (dual of [842, 740, 38]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(27100, 842, F27, 36) (dual of [842, 742, 37]-code) | [i] | ||
| 3 | Linear OOA(2732, 55, F27, 2, 18) (dual of [(55, 2), 78, 19]-NRT-code) | [i] | OOA Folding | |