Information on Result #1198064
Digital (81, 98, 1048667)-net over F27, using net defined by OOA based on linear OOA(2798, 1048667, F27, 18, 17) (dual of [(1048667, 18), 18875908, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(2798, 4194669, F27, 2, 17) (dual of [(4194669, 2), 8389240, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2798, 4194670, F27, 2, 17) (dual of [(4194670, 2), 8389242, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2717, 369, F27, 2, 8) (dual of [(369, 2), 721, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2717, 738, F27, 8) (dual of [738, 721, 9]-code), using
- construction XX applied to C1 = C([725,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([725,4]) [i] based on
- linear OA(2713, 728, F27, 7) (dual of [728, 715, 8]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,3}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(279, 728, F27, 5) (dual of [728, 719, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2715, 728, F27, 8) (dual of [728, 713, 9]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−3,−2,…,4}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(277, 728, F27, 4) (dual of [728, 721, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [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([725,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([725,4]) [i] based on
- OOA 2-folding [i] based on linear OA(2717, 738, F27, 8) (dual of [738, 721, 9]-code), using
- linear OOA(2781, 4194301, F27, 2, 17) (dual of [(4194301, 2), 8388521, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2781, 8388602, F27, 17) (dual of [8388602, 8388521, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2781, large, F27, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2781, large, F27, 17) (dual of [large, large−81, 18]-code), using
- OOA 2-folding [i] based on linear OA(2781, 8388602, F27, 17) (dual of [8388602, 8388521, 18]-code), using
- linear OOA(2717, 369, F27, 2, 8) (dual of [(369, 2), 721, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2798, 4194670, F27, 2, 17) (dual of [(4194670, 2), 8389242, 18]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.