Information on Result #1301014

Linear OA(4237, 4194377, F4, 27) (dual of [4194377, 4194140, 28]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4231, 4194368, F4, 27) (dual of [4194368, 4194137, 28]-code), using
    • construction X applied to Ce(26) ⊂ Ce(20) [i] based on
      1. linear OA(4221, 4194304, F4, 27) (dual of [4194304, 4194083, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
      2. linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      3. linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
        • an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  2. linear OA(4231, 4194371, F4, 23) (dual of [4194371, 4194140, 24]-code), using Gilbert–VarÅ¡amov bound and bm = 4231 > Vbs−1(k−1) = 1394 909712 839639 689877 012880 571154 306681 971593 350993 680159 929891 602366 611528 678199 163433 889197 732002 230263 985689 205759 637869 603136 020656 [i]
  3. linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), 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

None.