Information on Result #1303458

Linear OA(9122, 4783015, F9, 19) (dual of [4783015, 4782893, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(9120, 4783011, F9, 19) (dual of [4783011, 4782891, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(12) [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(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(97, 42, F9, 5) (dual of [42, 35, 6]-code), using
  2. linear OA(9120, 4783013, F9, 18) (dual of [4783013, 4782893, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 9120 > Vbs−1(k−1) = 2 271820 979786 716051 824536 673470 408417 084553 375315 031398 533400 827447 232085 368185 227728 375755 193646 017289 000316 101281 [i]
  3. linear OA(90, 2, F9, 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(9122, 4783015, F9, 2, 19) (dual of [(4783015, 2), 9565908, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(9122, 4783015, F9, 3, 19) (dual of [(4783015, 3), 14348923, 20]-NRT-code) [i]
3Digital (103, 122, 4783015)-net over F9 [i]
4Linear OOA(9122, 2391507, F9, 2, 19) (dual of [(2391507, 2), 4782892, 20]-NRT-code) [i]OOA Folding