Information on Result #1300229

Linear OA(4141, 4194346, F4, 17) (dual of [4194346, 4194205, 18]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4138, 4194342, F4, 17) (dual of [4194342, 4194204, 18]-code), using
    • construction X applied to Ce(16) ⊂ Ce(12) [i] based on
      1. linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      2. linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
  2. linear OA(4138, 4194343, F4, 14) (dual of [4194343, 4194205, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 4138 > Vbs−1(k−1) = 31835 983990 687787 275310 037479 813300 157579 048339 096316 674182 526255 471606 781623 223612 [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(4141, 2097173, F4, 2, 17) (dual of [(2097173, 2), 4194205, 18]-NRT-code) [i]OOA Folding