Information on Result #1301893

Linear OA(5140, 78181, F5, 23) (dual of [78181, 78041, 24]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5139, 78179, F5, 23) (dual of [78179, 78040, 24]-code), using
    • construction X applied to Ce(22) ⊂ Ce(15) [i] based on
      1. linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
      2. linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(512, 54, F5, 6) (dual of [54, 42, 7]-code), using
  2. linear OA(5139, 78180, F5, 22) (dual of [78180, 78041, 23]-code), using Gilbert–VarÅ¡amov bound and bm = 5139 > Vbs−1(k−1) = 488282 018122 615488 776625 588723 256827 563722 393840 563813 717573 349059 141483 832043 660451 166042 939645 [i]
  3. linear OA(50, 1, F5, 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(5140, 78181, F5, 2, 23) (dual of [(78181, 2), 156222, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5140, 78181, F5, 3, 23) (dual of [(78181, 3), 234403, 24]-NRT-code) [i]
3Digital (117, 140, 78181)-net over F5 [i]