Information on Result #1300082

Linear OA(4117, 262180, F4, 17) (dual of [262180, 262063, 18]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4114, 262176, F4, 17) (dual of [262176, 262062, 18]-code), using
    • construction X applied to Ce(16) ⊂ Ce(12) [i] based on
      1. linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      2. linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
  2. linear OA(4114, 262177, F4, 14) (dual of [262177, 262063, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 4114 > Vbs−1(k−1) = 7 077536 142071 768841 898351 771288 368189 050973 506714 868838 032300 649069 [i]
  3. linear OA(42, 3, F4, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), 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(4117, 131090, F4, 2, 17) (dual of [(131090, 2), 262063, 18]-NRT-code) [i]OOA Folding