Information on Result #866879
Linear OOA(2772, 369, F27, 2, 37) (dual of [(369, 2), 666, 38]-NRT-code), using OOA 2-folding based on linear OA(2772, 738, F27, 37) (dual of [738, 666, 38]-code), using
- construction XX applied to C1 = C([725,32]), C2 = C([0,33]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([725,33]) [i] based on
- linear OA(2768, 728, F27, 36) (dual of [728, 660, 37]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,32}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2764, 728, F27, 34) (dual of [728, 664, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2770, 728, F27, 37) (dual of [728, 658, 38]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,33}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2762, 728, F27, 33) (dual of [728, 666, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(272, 8, F27, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), 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 OOA(27101, 465, F27, 2, 37) (dual of [(465, 2), 829, 38]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |