Information on Result #1300223

Linear OA(4139, 262202, F4, 19) (dual of [262202, 262063, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4137, 262199, F4, 19) (dual of [262199, 262062, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(12) [i] based on
      1. linear OA(4127, 262144, F4, 19) (dual of [262144, 262017, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(410, 55, F4, 5) (dual of [55, 45, 6]-code), using
  2. linear OA(4137, 262200, F4, 17) (dual of [262200, 262063, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 4137 > Vbs−1(k−1) = 1026 188269 346711 708630 401001 138860 392669 968426 955614 068919 292981 293602 173543 753211 [i]
  3. linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-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(4139, 131101, F4, 2, 19) (dual of [(131101, 2), 262063, 20]-NRT-code) [i]OOA Folding