Information on Result #1195440
Digital (83, 102, 116518)-net over F16, using net defined by OOA based on linear OOA(16102, 116518, F16, 19, 19) (dual of [(116518, 19), 2213740, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(16102, 1048663, F16, 19) (dual of [1048663, 1048561, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(16102, 1048670, F16, 19) (dual of [1048670, 1048568, 20]-code), using
- (u, u+v)-construction [i] based on
- linear OA(1616, 89, F16, 9) (dual of [89, 73, 10]-code), using
- construction XX applied to C1 = C([5,12]), C2 = C([4,11]), C3 = C1 + C2 = C([5,11]), and C∩ = C1 ∩ C2 = C([4,12]) [i] based on
- linear OA(1614, 85, F16, 8) (dual of [85, 71, 9]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {5,6,…,12}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1614, 85, F16, 8) (dual of [85, 71, 9]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {4,5,…,11}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1616, 85, F16, 9) (dual of [85, 69, 10]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {4,5,…,12}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1612, 85, F16, 7) (dual of [85, 73, 8]-code), using the BCH-code C(I) with length 85 | 162−1, defining interval I = {5,6,…,11}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([5,12]), C2 = C([4,11]), C3 = C1 + C2 = C([5,11]), and C∩ = C1 ∩ C2 = C([4,12]) [i] based on
- linear OA(1686, 1048581, F16, 19) (dual of [1048581, 1048495, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(1616, 89, F16, 9) (dual of [89, 73, 10]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(16102, 1048670, F16, 19) (dual of [1048670, 1048568, 20]-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.