Information on Result #674932

Linear OA(3137, 59085, F3, 20) (dual of [59085, 58948, 21]-code), using construction X applied to Ce(19) ⊂ Ce(15) based on
  1. linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(3138, 59086, F3, 20) (dual of [59086, 58948, 21]-code) [i]Code Embedding in Larger Space
2Linear OA(3139, 59087, F3, 20) (dual of [59087, 58948, 21]-code) [i]
3Linear OA(3140, 59088, F3, 20) (dual of [59088, 58948, 21]-code) [i]
4Linear OA(3141, 59089, F3, 20) (dual of [59089, 58948, 21]-code) [i]
5Linear OA(3141, 59090, F3, 20) (dual of [59090, 58949, 21]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(3137, 29542, F3, 2, 20) (dual of [(29542, 2), 58947, 21]-NRT-code) [i]OOA Folding
7Linear OOA(3137, 19695, F3, 3, 20) (dual of [(19695, 3), 58948, 21]-NRT-code) [i]
8Linear OOA(3137, 14771, F3, 4, 20) (dual of [(14771, 4), 58947, 21]-NRT-code) [i]
9Linear OOA(3137, 11817, F3, 5, 20) (dual of [(11817, 5), 58948, 21]-NRT-code) [i]
10Linear OOA(3137, 5908, F3, 20, 20) (dual of [(5908, 20), 118023, 21]-NRT-code) [i]OA Folding and Stacking