Information on Result #1303703

Linear OA(1679, 1048595, F16, 16) (dual of [1048595, 1048516, 17]-code), using construction X with VarÅ¡amov bound based on
  1. 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
        1. 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]
        2. 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]
        3. 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
  2. linear OA(1678, 1048594, F16, 15) (dual of [1048594, 1048516, 16]-code), using Gilbert–VarÅ¡amov bound and bm = 1678 > Vbs−1(k−1) = 650622 878339 974728 321219 378393 058284 886491 433245 170642 370488 307256 660131 304835 129819 326696 [i]
  3. linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(1679, 1048595, F16, 2, 16) (dual of [(1048595, 2), 2097111, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (63, 79, 1048595)-net over F16 [i]