Information on Result #1303442

Linear OA(9118, 4783003, F9, 18) (dual of [4783003, 4782885, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(9117, 4783001, F9, 18) (dual of [4783001, 4782884, 19]-code), using
    • construction X applied to Ce(18) ⊂ Ce(13) [i] based on
      1. linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
      3. linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
  2. linear OA(9117, 4783002, F9, 17) (dual of [4783002, 4782885, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 9117 > Vbs−1(k−1) = 1 009292 463814 366584 286158 708107 182248 611649 524185 002343 876765 173304 388577 561308 203842 006942 323565 812557 656009 [i]
  3. linear OA(90, 1, F9, 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(9118, 4783003, F9, 2, 18) (dual of [(4783003, 2), 9565888, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(9118, 4783003, F9, 3, 18) (dual of [(4783003, 3), 14348891, 19]-NRT-code) [i]
3Digital (100, 118, 4783003)-net over F9 [i]