Information on Result #1301169

Linear OA(4259, 65607, F4, 40) (dual of [65607, 65348, 41]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4254, 65598, F4, 40) (dual of [65598, 65344, 41]-code), using
    • construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
      1. linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
      2. 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]
      3. linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
  2. linear OA(4254, 65602, F4, 38) (dual of [65602, 65348, 39]-code), using Gilbert–VarÅ¡amov bound and bm = 4254 > Vbs−1(k−1) = 544 638530 026979 625254 010437 073021 020957 259235 678673 746597 176819 082196 406846 073111 833970 730405 871882 352035 117349 974261 159102 319082 112544 397352 286758 670732 [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(4259, 32803, F4, 2, 40) (dual of [(32803, 2), 65347, 41]-NRT-code) [i]OOA Folding