Information on Result #1801924
Digital (63, 79, 1048595)-net over F16, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(1679, 1048595, F16, 16) (dual of [1048595, 1048516, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1678, 1048593, F16, 16) (dual of [1048593, 1048515, 17]-code), using
- 1 times truncation [i] based on linear OA(1679, 1048594, F16, 17) (dual of [1048594, 1048515, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- 1 times truncation [i] based on linear OA(1679, 1048594, F16, 17) (dual of [1048594, 1048515, 18]-code), using
- linear OA(1678, 1048594, F16, 15) (dual of [1048594, 1048516, 16]-code), using Gilbert–Varšamov bound and bm = 1678 > Vbs−1(k−1) = 650622 878339 974728 321219 378393 058284 886491 433245 170642 370488 307256 660131 304835 129819 326696 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 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(1678, 1048593, F16, 16) (dual of [1048593, 1048515, 17]-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.