Information on Result #1301740

Linear OA(5112, 78181, F5, 18) (dual of [78181, 78069, 19]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5111, 78179, F5, 18) (dual of [78179, 78068, 19]-code), using
    • construction X applied to Ce(17) ⊂ Ce(10) [i] based on
      1. linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(512, 54, F5, 6) (dual of [54, 42, 7]-code), using
  2. linear OA(5111, 78180, F5, 17) (dual of [78180, 78069, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 5111 > Vbs−1(k−1) = 399 151356 151647 618143 763208 153328 899826 104266 182399 537530 802971 890579 628285 [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(5112, 78181, F5, 2, 18) (dual of [(78181, 2), 156250, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5112, 78181, F5, 3, 18) (dual of [(78181, 3), 234431, 19]-NRT-code) [i]
3Digital (94, 112, 78181)-net over F5 [i]