Information on Result #1197392
Digital (40, 48, 2102091)-net over F27, using net defined by OOA based on linear OOA(2748, 2102091, F27, 10, 8) (dual of [(2102091, 10), 21020862, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2748, 4204183, F27, 2, 8) (dual of [(4204183, 2), 8408318, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2712, 9882, F27, 2, 4) (dual of [(9882, 2), 19752, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2712, 19764, F27, 4) (dual of [19764, 19752, 5]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(270, 732, F27, 0) (dual of [732, 732, 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
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code) (see above)
- linear OA(271, 732, F27, 1) (dual of [732, 731, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(271, 732, F27, 1) (dual of [732, 731, 2]-code) (see above)
- linear OA(273, 732, F27, 2) (dual of [732, 729, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(273, 757, F27, 2) (dual of [757, 754, 3]-code), using
- Hamming code H(3,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 757, F27, 2) (dual of [757, 754, 3]-code), using
- linear OA(277, 732, F27, 4) (dual of [732, 725, 5]-code), using
- construction XX applied to C1 = C([727,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([727,2]) [i] based on
- linear OA(275, 728, F27, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(275, 728, F27, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(277, 728, F27, 4) (dual of [728, 721, 5]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- 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 (see above)
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([727,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([727,2]) [i] based on
- linear OA(270, 732, F27, 0) (dual of [732, 732, 1]-code), using
- generalized (u, u+v)-construction [i] based on
- OOA 2-folding [i] based on linear OA(2712, 19764, F27, 4) (dual of [19764, 19752, 5]-code), using
- linear OOA(2736, 4194301, F27, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2736, 8388602, F27, 8) (dual of [8388602, 8388566, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2736, large, F27, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2736, large, F27, 8) (dual of [large, large−36, 9]-code), using
- OOA 2-folding [i] based on linear OA(2736, 8388602, F27, 8) (dual of [8388602, 8388566, 9]-code), using
- linear OOA(2712, 9882, F27, 2, 4) (dual of [(9882, 2), 19752, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
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.