Information on Result #1324246

Linear OA(4251, 65628, F4, 38) (dual of [65628, 65377, 39]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4249, 65624, F4, 38) (dual of [65624, 65375, 39]-code), using
    • construction X applied to Ce(37) ⊂ Ce(26) [i] based on
      1. linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
      2. linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
      3. linear OA(424, 88, F4, 10) (dual of [88, 64, 11]-code), using
  2. linear OA(4249, 65626, F4, 37) (dual of [65626, 65377, 38]-code), using Gilbert–VarÅ¡amov bound and bm = 4249 > Vbs−1(k−1) = 103808 973300 366592 314332 094137 619346 086037 747598 309036 024469 684879 650426 039868 877548 919250 796491 391265 053624 899410 906359 079751 729178 475217 563193 392876 [i]
  3. linear OA(40, 2, F4, 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(4251, 65628, F4, 2, 38) (dual of [(65628, 2), 131005, 39]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4251, 65628, F4, 3, 38) (dual of [(65628, 3), 196633, 39]-NRT-code) [i]
3Digital (213, 251, 65628)-net over F4 [i]
4Linear OOA(4251, 32814, F4, 2, 38) (dual of [(32814, 2), 65377, 39]-NRT-code) [i]OOA Folding