Information on Result #1197414
Digital (13, 22, 201)-net over F27, using net defined by OOA based on linear OOA(2722, 201, F27, 10, 9) (dual of [(201, 10), 1988, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2722, 403, F27, 2, 9) (dual of [(403, 2), 784, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2722, 404, F27, 2, 9) (dual of [(404, 2), 786, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(275, 38, F27, 2, 4) (dual of [(38, 2), 71, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,71P) [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- linear OOA(2717, 366, F27, 2, 9) (dual of [(366, 2), 715, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2717, 732, F27, 9) (dual of [732, 715, 10]-code), using
- construction XX applied to C1 = C([727,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([727,7]) [i] based on
- 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 = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2715, 728, F27, 8) (dual of [728, 713, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2717, 728, F27, 9) (dual of [728, 711, 10]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2713, 728, F27, 7) (dual of [728, 715, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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, using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([727,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([727,7]) [i] based on
- OOA 2-folding [i] based on linear OA(2717, 732, F27, 9) (dual of [732, 715, 10]-code), using
- linear OOA(275, 38, F27, 2, 4) (dual of [(38, 2), 71, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2722, 404, F27, 2, 9) (dual of [(404, 2), 786, 10]-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.