Information on Result #1300589

Linear OA(4185, 16446, F4, 32) (dual of [16446, 16261, 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, 16443, F4, 31) (dual of [16443, 16261, 32]-code), using Gilbert–VarÅ¡amov bound and bm = 4182 > Vbs−1(k−1) = 2 277113 684771 857228 524908 643950 504284 563837 243592 415876 870514 007819 190424 282275 896976 604567 345972 185866 866544 [i]
  3. linear OA(40, 3, F4, 0) (dual of [3, 3, 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(4185, 16446, F4, 2, 32) (dual of [(16446, 2), 32707, 33]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4185, 16446, F4, 3, 32) (dual of [(16446, 3), 49153, 33]-NRT-code) [i]
3Digital (153, 185, 16446)-net over F4 [i]
4Linear OOA(4185, 8223, F4, 2, 32) (dual of [(8223, 2), 16261, 33]-NRT-code) [i]OOA Folding