Information on Result #682213

Linear OA(5149, 1953192, F5, 19) (dual of [1953192, 1953043, 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(513, 67, F5, 6) (dual of [67, 54, 7]-code), using

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(5150, 1953193, F5, 19) (dual of [1953193, 1953043, 20]-code) [i]Code Embedding in Larger Space
2Linear OOA(5149, 1953192, F5, 2, 19) (dual of [(1953192, 2), 3906235, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(5149, 1953192, F5, 3, 19) (dual of [(1953192, 3), 5859427, 20]-NRT-code) [i]
4Digital (130, 149, 1953192)-net over F5 [i]
5Linear OA(5150, 1953194, F5, 19) (dual of [1953194, 1953044, 20]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(5149, 976596, F5, 2, 19) (dual of [(976596, 2), 1953043, 20]-NRT-code) [i]OOA Folding
7Linear OOA(5149, 651064, F5, 3, 19) (dual of [(651064, 3), 1953043, 20]-NRT-code) [i]
8Linear OOA(5149, 217021, F5, 19, 19) (dual of [(217021, 19), 4123250, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row