Information on Result #1300729

Linear OA(4203, 4194376, F4, 23) (dual of [4194376, 4194173, 24]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4198, 4194368, F4, 23) (dual of [4194368, 4194170, 24]-code), using
    • construction X applied to Ce(22) ⊂ Ce(16) [i] based on
      1. linear OA(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
      2. 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]
      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(4198, 4194371, F4, 20) (dual of [4194371, 4194173, 21]-code), using Gilbert–VarÅ¡amov bound and bm = 4198 > Vbs−1(k−1) = 6469 343317 032029 937929 727414 243528 500194 072294 532267 849547 340804 498727 741441 335217 081465 199220 122349 300037 753218 335280 [i]
  3. linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-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

None.