Information on Result #1302306

Linear OA(7100, 117690, F7, 18) (dual of [117690, 117590, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(798, 117686, F7, 18) (dual of [117686, 117588, 19]-code), using
    • construction X applied to Ce(17) ⊂ Ce(11) [i] based on
      1. linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
      3. linear OA(77, 37, F7, 5) (dual of [37, 30, 6]-code), using
  2. linear OA(798, 117688, F7, 17) (dual of [117688, 117590, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 798 > Vbs−1(k−1) = 182 399347 647397 568005 117739 585778 309681 584529 696909 753113 273226 663512 594091 425911 [i]
  3. linear OA(70, 2, F7, 0) (dual of [2, 2, 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(7100, 117690, F7, 2, 18) (dual of [(117690, 2), 235280, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(7100, 117690, F7, 3, 18) (dual of [(117690, 3), 352970, 19]-NRT-code) [i]
3Digital (82, 100, 117690)-net over F7 [i]
4Linear OOA(7100, 58845, F7, 2, 18) (dual of [(58845, 2), 117590, 19]-NRT-code) [i]OOA Folding