Information on Result #682212

Linear OA(5148, 1953188, F5, 19) (dual of [1953188, 1953040, 20]-code), using construction X applied to Ce(18) ⊂ Ce(11) based on
  1. linear OA(5136, 1953125, F5, 19) (dual of [1953125, 1952989, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(582, 1953125, F5, 12) (dual of [1953125, 1953043, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(512, 63, F5, 6) (dual of [63, 51, 7]-code), using
    • the BCH-code C(I) with length 63 | 56−1, defining interval I = {−5,−3,−1,…,5}, and designed minimum distance d ≥ |I|+1 = 7 [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 OOA(5148, 1953188, F5, 2, 19) (dual of [(1953188, 2), 3906228, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5148, 1953188, F5, 3, 19) (dual of [(1953188, 3), 5859416, 20]-NRT-code) [i]
3Digital (129, 148, 1953188)-net over F5 [i]
4Linear OOA(5148, 976594, F5, 2, 19) (dual of [(976594, 2), 1953040, 20]-NRT-code) [i]OOA Folding
5Linear OOA(5148, 651062, F5, 3, 19) (dual of [(651062, 3), 1953038, 20]-NRT-code) [i]