Information on Result #1324372

Linear OA(8163, 2097219, F8, 25) (dual of [2097219, 2097056, 26]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8160, 2097213, F8, 25) (dual of [2097213, 2097053, 26]-code), using
    • construction X applied to Ce(24) ⊂ Ce(16) [i] based on
      1. linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      2. linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      3. linear OA(812, 61, F8, 7) (dual of [61, 49, 8]-code), using
  2. linear OA(8160, 2097216, F8, 24) (dual of [2097216, 2097056, 25]-code), using Gilbert–VarÅ¡amov bound and bm = 8160 > Vbs−1(k−1) = 26454 329089 122927 666356 732923 211204 393819 153547 701684 013992 386080 763091 073788 613895 327257 012476 284163 674462 656726 772297 145728 782975 487465 511192 [i]
  3. linear OA(80, 3, F8, 0) (dual of [3, 3, 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(8163, 2097219, F8, 2, 25) (dual of [(2097219, 2), 4194275, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8163, 2097219, F8, 3, 25) (dual of [(2097219, 3), 6291494, 26]-NRT-code) [i]
3Digital (138, 163, 2097219)-net over F8 [i]