Information on Result #1300803

Linear OA(4210, 65605, F4, 32) (dual of [65605, 65395, 33]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4206, 65598, F4, 32) (dual of [65598, 65392, 33]-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(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
  2. linear OA(4206, 65601, F4, 30) (dual of [65601, 65395, 31]-code), using Gilbert–VarÅ¡amov bound and bm = 4206 > Vbs−1(k−1) = 378 063445 910169 287780 851243 288746 393388 862067 837477 147442 348633 234238 368827 366501 500326 990493 218383 463918 372649 254243 238653 [i]
  3. linear OA(41, 4, F4, 1) (dual of [4, 3, 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(4210, 32802, F4, 2, 32) (dual of [(32802, 2), 65394, 33]-NRT-code) [i]OOA Folding