Information on Result #1303352

Linear OA(997, 4783003, F9, 15) (dual of [4783003, 4782906, 16]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(996, 4783001, F9, 15) (dual of [4783001, 4782905, 16]-code), using
    • construction X applied to Ce(14) ⊂ Ce(10) [i] based on
      1. linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
      2. linear OA(964, 4782969, F9, 11) (dual of [4782969, 4782905, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(996, 4783002, F9, 14) (dual of [4783002, 4782906, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 996 > Vbs−1(k−1) = 60532 514037 312329 010299 216538 064110 495898 884390 405791 188430 274537 817394 175196 622687 678409 [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(997, 4783003, F9, 2, 15) (dual of [(4783003, 2), 9565909, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(997, 4783003, F9, 3, 15) (dual of [(4783003, 3), 14348912, 16]-NRT-code) [i]
3Digital (82, 97, 4783003)-net over F9 [i]