Information on Result #1301107

Linear OA(4246, 16441, F4, 44) (dual of [16441, 16195, 45]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4245, 16439, F4, 44) (dual of [16439, 16194, 45]-code), using
    • construction X applied to Ce(44) ⊂ Ce(36) [i] based on
      1. linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
      2. linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
      3. linear OA(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
  2. linear OA(4245, 16440, F4, 43) (dual of [16440, 16195, 44]-code), using Gilbert–VarÅ¡amov bound and bm = 4245 > Vbs−1(k−1) = 86 255439 833587 769115 546280 187470 614841 074447 503624 857998 096348 267507 577990 581222 545492 634860 194345 453600 888024 467279 216903 315092 704224 773718 491482 [i]
  3. linear OA(40, 1, F4, 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(4246, 16441, F4, 2, 44) (dual of [(16441, 2), 32636, 45]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4246, 16441, F4, 3, 44) (dual of [(16441, 3), 49077, 45]-NRT-code) [i]
3Digital (202, 246, 16441)-net over F4 [i]