Information on Result #1302552

Linear OA(872, 262174, F8, 13) (dual of [262174, 262102, 14]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(871, 262172, F8, 13) (dual of [262172, 262101, 14]-code), using
    • construction X applied to Ce(12) ⊂ Ce(8) [i] based on
      1. linear OA(867, 262144, F8, 13) (dual of [262144, 262077, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(84, 28, F8, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,8)), using
  2. linear OA(871, 262173, F8, 12) (dual of [262173, 262102, 13]-code), using Gilbert–VarÅ¡amov bound and bm = 871 > Vbs−1(k−1) = 19 919736 703235 728401 330460 600398 153201 426623 138547 709174 107481 [i]
  3. linear OA(80, 1, F8, 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(872, 262174, F8, 2, 13) (dual of [(262174, 2), 524276, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(872, 262174, F8, 3, 13) (dual of [(262174, 3), 786450, 14]-NRT-code) [i]
3Digital (59, 72, 262174)-net over F8 [i]
4Linear OOA(872, 131087, F8, 2, 13) (dual of [(131087, 2), 262102, 14]-NRT-code) [i]OOA Folding