Information on Result #1300832

Linear OA(4214, 65609, F4, 33) (dual of [65609, 65395, 34]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4209, 65601, F4, 33) (dual of [65601, 65392, 34]-code), using
    • construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
      1. linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
      2. linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
      3. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
        • an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  2. linear OA(4209, 65604, F4, 30) (dual of [65604, 65395, 31]-code), using Gilbert–VarÅ¡amov bound and bm = 4209 > Vbs−1(k−1) = 378 565266 795996 793022 482967 872745 898458 528005 784132 214420 395626 712269 691416 635387 284520 286688 620681 732373 152125 074612 605792 [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.