Information on Result #1302631

Linear OA(889, 524306, F8, 15) (dual of [524306, 524217, 16]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(888, 524304, F8, 15) (dual of [524304, 524216, 16]-code), using
    • trace code [i] based on linear OA(6444, 262152, F64, 15) (dual of [262152, 262108, 16]-code), using
      • construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
        1. linear OA(6443, 262145, F64, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
        2. linear OA(6437, 262145, F64, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
        3. linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
  2. linear OA(888, 524305, F8, 14) (dual of [524305, 524217, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 888 > Vbs−1(k−1) = 3519 754360 311078 247598 767231 296367 212708 937478 219662 564852 787360 440423 975191 [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(889, 524306, F8, 2, 15) (dual of [(524306, 2), 1048523, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(889, 524306, F8, 3, 15) (dual of [(524306, 3), 1572829, 16]-NRT-code) [i]
3Digital (74, 89, 524306)-net over F8 [i]
4Linear OOA(889, 262153, F8, 2, 15) (dual of [(262153, 2), 524217, 16]-NRT-code) [i]OOA Folding