Information on Result #737527

Linear OA(5129, 78169, F5, 22) (dual of [78169, 78040, 23]-code), using construction X applied to Ce(21) ⊂ Ce(15) based on
  1. linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(59, 44, F5, 5) (dual of [44, 35, 6]-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(5131, 78171, F5, 22) (dual of [78171, 78040, 23]-code) [i]Code Embedding in Larger Space
2Linear OA(5132, 78172, F5, 22) (dual of [78172, 78040, 23]-code) [i]
3Linear OA(5133, 78173, F5, 22) (dual of [78173, 78040, 23]-code) [i]
4Linear OOA(5129, 61738, F5, 2, 22) (dual of [(61738, 2), 123347, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(5129, 61738, F5, 3, 22) (dual of [(61738, 3), 185085, 23]-NRT-code) [i]
6Digital (107, 129, 61738)-net over F5 [i]
7Linear OA(5131, 78172, F5, 22) (dual of [78172, 78041, 23]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(5132, 78174, F5, 22) (dual of [78174, 78042, 23]-code) [i]
9Linear OA(5133, 78176, F5, 22) (dual of [78176, 78043, 23]-code) [i]
10Linear OA(5134, 78178, F5, 22) (dual of [78178, 78044, 23]-code) [i]
11Linear OOA(5129, 39084, F5, 2, 22) (dual of [(39084, 2), 78039, 23]-NRT-code) [i]OOA Folding
12Linear OOA(5129, 26056, F5, 3, 22) (dual of [(26056, 3), 78039, 23]-NRT-code) [i]
13Linear OOA(5129, 7106, F5, 22, 22) (dual of [(7106, 22), 156203, 23]-NRT-code) [i]OA Folding and Stacking