Information on Result #1300585

Linear OA(4183, 16442, F4, 32) (dual of [16442, 16259, 33]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4182, 16440, F4, 32) (dual of [16440, 16258, 33]-code), using
    • construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
      1. linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
      2. linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
      3. linear OA(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
  2. linear OA(4182, 16441, F4, 31) (dual of [16441, 16259, 32]-code), using Gilbert–VarÅ¡amov bound and bm = 4182 > Vbs−1(k−1) = 2 268811 558949 293422 422571 069668 397283 457733 507637 923233 673591 835947 164213 946139 959695 019896 441186 152573 689004 [i]
  3. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-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(4183, 16442, F4, 2, 32) (dual of [(16442, 2), 32701, 33]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4183, 16442, F4, 3, 32) (dual of [(16442, 3), 49143, 33]-NRT-code) [i]
3Digital (151, 183, 16442)-net over F4 [i]
4Linear OOA(4183, 8221, F4, 2, 32) (dual of [(8221, 2), 16259, 33]-NRT-code) [i]OOA Folding