Information on Result #733100
Linear OA(27104, 834, F27, 38) (dual of [834, 730, 39]-code), using (u, u+v)-construction based on
- linear OA(2730, 96, F27, 19) (dual of [96, 66, 20]-code), using
- extended algebraic-geometric code AGe(F,76P) [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- linear OA(2774, 738, F27, 38) (dual of [738, 664, 39]-code), using
- construction XX applied to C1 = C([725,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([725,34]) [i] based on
- 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(2766, 728, F27, 35) (dual of [728, 662, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2772, 728, F27, 38) (dual of [728, 656, 39]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,34}, and designed minimum distance d ≥ |I|+1 = 39 [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(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
- construction XX applied to C1 = C([725,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([725,34]) [i] based on
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(27104, 417, F27, 2, 38) (dual of [(417, 2), 730, 39]-NRT-code) | [i] | OOA Folding | |