Information on Result #1302329

Linear OA(7103, 117682, F7, 19) (dual of [117682, 117579, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(7101, 117678, F7, 19) (dual of [117678, 117577, 20]-code), using
    • construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
      1. linear OA(797, 117650, F7, 19) (dual of [117650, 117553, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
      2. linear OA(773, 117650, F7, 15) (dual of [117650, 117577, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
      3. linear OA(74, 28, F7, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,7)), using
  2. linear OA(7101, 117680, F7, 18) (dual of [117680, 117579, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 7101 > Vbs−1(k−1) = 7 566477 494903 534340 314654 930375 305747 835375 897299 411454 002532 354326 885301 636888 100151 [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(7103, 117682, F7, 2, 19) (dual of [(117682, 2), 235261, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(7103, 117682, F7, 3, 19) (dual of [(117682, 3), 352943, 20]-NRT-code) [i]
3Digital (84, 103, 117682)-net over F7 [i]
4Linear OOA(7103, 58841, F7, 2, 19) (dual of [(58841, 2), 117579, 20]-NRT-code) [i]OOA Folding