Information on Result #1745282
Digital (50, 89, 629)-net over F64, using net defined by OOA based on linear OOA(6489, 629, F64, 45, 39) (dual of [(629, 45), 28216, 40]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OOA(6489, 4404, F64, 3, 39) (dual of [(4404, 3), 13123, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6489, 4409, F64, 3, 39) (dual of [(4409, 3), 13138, 40]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6489, 4409, F64, 39) (dual of [4409, 4320, 40]-code), using
- 299 step Varšamov–Edel lengthening with (ri) = (6, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 38 times 0, 1, 76 times 0, 1, 147 times 0) [i] based on linear OA(6477, 4098, F64, 39) (dual of [4098, 4021, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- linear OA(6477, 4096, F64, 39) (dual of [4096, 4019, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(6475, 4096, F64, 38) (dual of [4096, 4021, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(38) ⊂ Ce(37) [i] based on
- 299 step Varšamov–Edel lengthening with (ri) = (6, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 19 times 0, 1, 38 times 0, 1, 76 times 0, 1, 147 times 0) [i] based on linear OA(6477, 4098, F64, 39) (dual of [4098, 4021, 40]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6489, 4409, F64, 39) (dual of [4409, 4320, 40]-code), using
- discarding factors / shortening the dual code based on linear OOA(6489, 4409, F64, 3, 39) (dual of [(4409, 3), 13138, 40]-NRT-code), using
Mode: 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.