Information on Result #682476

Linear OA(5137, 78149, F5, 24) (dual of [78149, 78012, 25]-code), using construction X applied to Ce(23) ⊂ Ce(20) based on
  1. linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
  2. linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(5138, 78150, F5, 24) (dual of [78150, 78012, 25]-code) [i]Code Embedding in Larger Space
2Linear OOA(5137, 47376, F5, 2, 24) (dual of [(47376, 2), 94615, 25]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(5137, 47376, F5, 3, 24) (dual of [(47376, 3), 141991, 25]-NRT-code) [i]
4Digital (113, 137, 47376)-net over F5 [i]
5Linear OOA(5137, 39074, F5, 2, 24) (dual of [(39074, 2), 78011, 25]-NRT-code) [i]OOA Folding
6Linear OOA(5137, 26049, F5, 3, 24) (dual of [(26049, 3), 78010, 25]-NRT-code) [i]
7Linear OOA(5137, 6512, F5, 24, 24) (dual of [(6512, 24), 156151, 25]-NRT-code) [i]OA Folding and Stacking