Information on Result #682481

Linear OA(5109, 78149, F5, 19) (dual of [78149, 78040, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
  1. linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
    • the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]

Mode: Constructive and 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 OA(5110, 78150, F5, 19) (dual of [78150, 78040, 20]-code) [i]Code Embedding in Larger Space
2Linear OOA(5109, 49465, F5, 2, 19) (dual of [(49465, 2), 98821, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(5109, 49465, F5, 3, 19) (dual of [(49465, 3), 148286, 20]-NRT-code) [i]
4Digital (90, 109, 49465)-net over F5 [i]
5Linear OOA(5109, 39074, F5, 2, 19) (dual of [(39074, 2), 78039, 20]-NRT-code) [i]OOA Folding
6Linear OOA(5109, 26049, F5, 3, 19) (dual of [(26049, 3), 78038, 20]-NRT-code) [i]
7Linear OOA(5109, 8683, F5, 19, 19) (dual of [(8683, 19), 164868, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row