Information on Result #1300805

Linear OA(4211, 65607, F4, 32) (dual of [65607, 65396, 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, 65602, F4, 30) (dual of [65602, 65396, 31]-code), using Gilbert–VarÅ¡amov bound and bm = 4206 > Vbs−1(k−1) = 378 230648 133154 475780 207693 252119 461232 352922 298145 706430 238006 436037 430799 117165 068569 623147 008411 713569 229202 748836 607412 [i]
  3. linear OA(41, 5, F4, 1) (dual of [5, 4, 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(4211, 65607, F4, 2, 32) (dual of [(65607, 2), 131003, 33]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4211, 65607, F4, 3, 32) (dual of [(65607, 3), 196610, 33]-NRT-code) [i]
3Digital (179, 211, 65607)-net over F4 [i]
4Linear OOA(4211, 32803, F4, 2, 32) (dual of [(32803, 2), 65395, 33]-NRT-code) [i]OOA Folding