Information on Result #1302578

Linear OA(877, 8206, F8, 19) (dual of [8206, 8129, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(876, 8204, F8, 19) (dual of [8204, 8128, 20]-code), using
    • trace code [i] based on linear OA(6438, 4102, F64, 19) (dual of [4102, 4064, 20]-code), using
      • construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
        1. linear OA(6437, 4097, F64, 19) (dual of [4097, 4060, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
        2. linear OA(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
        3. linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(876, 8205, F8, 18) (dual of [8205, 8129, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 876 > Vbs−1(k−1) = 2 223099 089204 329555 148588 464101 294257 019462 533549 831781 618987 926016 [i]
  3. linear OA(80, 1, F8, 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(877, 8206, F8, 2, 19) (dual of [(8206, 2), 16335, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(877, 8206, F8, 3, 19) (dual of [(8206, 3), 24541, 20]-NRT-code) [i]
3Digital (58, 77, 8206)-net over F8 [i]
4Linear OOA(877, 4103, F8, 2, 19) (dual of [(4103, 2), 8129, 20]-NRT-code) [i]OOA Folding