Information on Result #682176

Linear OA(5139, 1953155, F5, 19) (dual of [1953155, 1953016, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) 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(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  3. linear OA(53, 30, F5, 2) (dual of [30, 27, 3]-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(5140, 1953156, F5, 19) (dual of [1953156, 1953016, 20]-code) [i]Code Embedding in Larger Space
2Linear OA(5141, 1953157, F5, 19) (dual of [1953157, 1953016, 20]-code) [i]
3Linear OA(5142, 1953158, F5, 19) (dual of [1953158, 1953016, 20]-code) [i]
4Linear OA(5141, 1953158, F5, 19) (dual of [1953158, 1953017, 20]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OA(5142, 1953160, F5, 19) (dual of [1953160, 1953018, 20]-code) [i]
6Linear OOA(5139, 976577, F5, 2, 19) (dual of [(976577, 2), 1953015, 20]-NRT-code) [i]OOA Folding
7Linear OOA(5139, 651051, F5, 3, 19) (dual of [(651051, 3), 1953014, 20]-NRT-code) [i]
8Linear OOA(5139, 217017, F5, 19, 19) (dual of [(217017, 19), 4123184, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row