Information on Result #1178988
Digital (54, 59, 7174473)-net over F3, using net defined by OOA based on linear OOA(359, 7174473, F3, 5, 5) (dual of [(7174473, 5), 35872306, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(359, 7174473, F3, 4, 5) (dual of [(7174473, 4), 28697833, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(31, 2391491, F3, 4, 1) (dual of [(2391491, 4), 9565963, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(31, s, F3, 4, 1) for arbitrarily large s, using
- appending 3 arbitrary columns [i] based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(31, s, F3, 4, 1) for arbitrarily large s, using
- linear OOA(315, 2391491, F3, 4, 2) (dual of [(2391491, 4), 9565949, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(315, 7174453, F3, 4, 2) (dual of [(7174453, 4), 28697797, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(315, 7174453, F3, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
- appending kth column [i] based on linear OA(315, 7174453, F3, 2) (dual of [7174453, 7174438, 3]-code), using
- Hamming code H(15,3) [i]
- appending kth column [i] based on linear OA(315, 7174453, F3, 2) (dual of [7174453, 7174438, 3]-code), using
- appending 2 arbitrary columns [i] based on linear OOA(315, 7174453, F3, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(315, 7174453, F3, 4, 2) (dual of [(7174453, 4), 28697797, 3]-NRT-code), using
- linear OOA(343, 2391491, F3, 4, 5) (dual of [(2391491, 4), 9565921, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- linear OOA(31, 2391491, F3, 4, 1) (dual of [(2391491, 4), 9565963, 2]-NRT-code), using
- generalized (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.