Information on Result #1303574

Linear OA(9143, 4783015, F9, 22) (dual of [4783015, 4782872, 23]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(9141, 4783011, F9, 22) (dual of [4783011, 4782870, 23]-code), using
    • construction X applied to Ce(21) ⊂ Ce(15) [i] based on
      1. linear OA(9134, 4782969, F9, 22) (dual of [4782969, 4782835, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
      2. linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(97, 42, F9, 5) (dual of [42, 35, 6]-code), using
  2. linear OA(9141, 4783013, F9, 21) (dual of [4783013, 4782872, 22]-code), using Gilbert–VarÅ¡amov bound and bm = 9141 > Vbs−1(k−1) = 18 607477 707935 013165 075750 689248 044807 559963 572580 979585 122447 462005 622181 938668 701710 896894 149022 771986 826389 514117 590437 936439 288481 [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(9143, 4783015, F9, 2, 22) (dual of [(4783015, 2), 9565887, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(9143, 4783015, F9, 3, 22) (dual of [(4783015, 3), 14348902, 23]-NRT-code) [i]
3Digital (121, 143, 4783015)-net over F9 [i]
4Linear OOA(9143, 2391507, F9, 2, 22) (dual of [(2391507, 2), 4782871, 23]-NRT-code) [i]OOA Folding