Information on Result #674587

Linear OA(3163, 531483, F3, 20) (dual of [531483, 531320, 21]-code), using construction X applied to Ce(19) ⊂ Ce(15) based on
  1. linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  3. linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-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(3164, 531484, F3, 20) (dual of [531484, 531320, 21]-code) [i]Code Embedding in Larger Space
2Linear OA(3165, 531485, F3, 20) (dual of [531485, 531320, 21]-code) [i]
3Linear OA(3166, 531486, F3, 20) (dual of [531486, 531320, 21]-code) [i]
4Linear OA(3167, 531487, F3, 20) (dual of [531487, 531320, 21]-code) [i]
5Linear OOA(3163, 265741, F3, 2, 20) (dual of [(265741, 2), 531319, 21]-NRT-code) [i]OOA Folding
6Linear OOA(3163, 177161, F3, 3, 20) (dual of [(177161, 3), 531320, 21]-NRT-code) [i]
7Linear OOA(3163, 132870, F3, 4, 20) (dual of [(132870, 4), 531317, 21]-NRT-code) [i]
8Linear OOA(3163, 106296, F3, 5, 20) (dual of [(106296, 5), 531317, 21]-NRT-code) [i]
9Linear OOA(3163, 53148, F3, 20, 20) (dual of [(53148, 20), 1062797, 21]-NRT-code) [i]OA Folding and Stacking