Information on Result #1302448

Linear OA(853, 8206, F8, 13) (dual of [8206, 8153, 14]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(852, 8204, F8, 13) (dual of [8204, 8152, 14]-code), using
    • trace code [i] based on linear OA(6426, 4102, F64, 13) (dual of [4102, 4076, 14]-code), using
      • construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
        1. linear OA(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
        2. linear OA(6421, 4097, F64, 11) (dual of [4097, 4076, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
        3. linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(852, 8205, F8, 12) (dual of [8205, 8153, 13]-code), using Gilbert–VarÅ¡amov bound and bm = 852 > Vbs−1(k−1) = 557 667598 560624 431571 643600 935683 193596 222431 [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(853, 8206, F8, 2, 13) (dual of [(8206, 2), 16359, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(853, 8206, F8, 3, 13) (dual of [(8206, 3), 24565, 14]-NRT-code) [i]
3Digital (40, 53, 8206)-net over F8 [i]
4Linear OOA(853, 4103, F8, 2, 13) (dual of [(4103, 2), 8153, 14]-NRT-code) [i]OOA Folding