Information on Result #1234110
Digital (45, 53, 4333407)-net over F49, using generalized (u, u+v)-construction based on
- digital (0, 1, 2451)-net over F49, using
- s-reduction based on digital (0, 1, s)-net over F49 for arbitrarily large s, using
- digital (0, 1, 2451)-net over F49 (see above)
- digital (0, 1, 2451)-net over F49 (see above)
- digital (1, 3, 2451)-net over F49, using
- digital (3, 5, 1441201)-net over F49, using
- s-reduction based on digital (3, 5, 5884901)-net over F49, using
- digital (9, 13, 1441201)-net over F49, using
- s-reduction based on digital (9, 13, 2882402)-net over F49, using
- net defined by OOA [i] based on linear OOA(4913, 2882402, F49, 4, 4) (dual of [(2882402, 4), 11529595, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4913, 2882402, F49, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(499, 5764801, F49, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(4913, 5764805, F49, 4) (dual of [5764805, 5764792, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(4913, 5764804, F49, 4) (dual of [5764804, 5764791, 5]-code), using
- appending kth column [i] based on linear OOA(4913, 2882402, F49, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(4913, 2882402, F49, 4, 4) (dual of [(2882402, 4), 11529595, 5]-NRT-code), using
- s-reduction based on digital (9, 13, 2882402)-net over F49, using
- digital (21, 29, 1441201)-net over F49, using
- net defined by OOA [i] based on linear OOA(4929, 1441201, F49, 8, 8) (dual of [(1441201, 8), 11529579, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(4929, 5764804, F49, 8) (dual of [5764804, 5764775, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4929, 5764805, F49, 8) (dual of [5764805, 5764776, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code) (see above)
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(4929, 5764805, F49, 8) (dual of [5764805, 5764776, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(4929, 5764804, F49, 8) (dual of [5764804, 5764775, 9]-code), using
- net defined by OOA [i] based on linear OOA(4929, 1441201, F49, 8, 8) (dual of [(1441201, 8), 11529579, 9]-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.