Information on Result #674935

Linear OA(3117, 59085, F3, 17) (dual of [59085, 58968, 18]-code), using construction X applied to Ce(16) ⊂ Ce(12) based on
  1. linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(381, 59049, F3, 13) (dual of [59049, 58968, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), 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(3118, 59086, F3, 17) (dual of [59086, 58968, 18]-code) [i]Code Embedding in Larger Space
2Linear OA(3119, 59087, F3, 17) (dual of [59087, 58968, 18]-code) [i]
3Linear OA(3120, 59088, F3, 17) (dual of [59088, 58968, 18]-code) [i]
4Linear OA(3121, 59089, F3, 17) (dual of [59089, 58968, 18]-code) [i]
5Linear OA(3121, 59090, F3, 17) (dual of [59090, 58969, 18]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(3117, 29542, F3, 2, 17) (dual of [(29542, 2), 58967, 18]-NRT-code) [i]OOA Folding
7Linear OOA(3117, 19695, F3, 3, 17) (dual of [(19695, 3), 58968, 18]-NRT-code) [i]
8Linear OOA(3117, 14771, F3, 4, 17) (dual of [(14771, 4), 58967, 18]-NRT-code) [i]
9Linear OOA(3117, 11817, F3, 5, 17) (dual of [(11817, 5), 58968, 18]-NRT-code) [i]
10Linear OOA(3117, 7385, F3, 17, 17) (dual of [(7385, 17), 125428, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row